Before you can ask questions, the Rehabilitation Training arc and Extended Natagumo Mountain Arc are effectively the same arc in this fic.
It'll be followed up by a proper standalone Butterfly Estate arc.

"Onii-chan! Wait up!" Nezuko said as she chased her older brother around the clearing in which their house stood, "Come on then! Catch me if you can!" he said in return as laughter filled the sky.

Years passed like that, they were happy, but after their father passed away Tanjiro saw it as his job to be the new man of the house, Nezuko understood, so she decided to help her mother with her duties, every so often Tanjiro would go to the nearby village to sell charcoal, just like their father did.

But that one night.
That one night felt like a stern needle pushed through her heart, the moment she opened the door her brother was shuffling towards her, he looked like he was hurt, seriously hurt, she wanted to call out, she did.

"Onii-chan!" she cried out, tears filled her eyes and her vision was hazy, but once it cleared up she noticed she wasn't on the mountains anymore, she quickly sat up and looked around, noticing she was in a hospital ward.

Her gaze scanned the room from left to right, and once she had turned to her right properly she saw someone, someone she recognized.

The blond-haired boy was sitting upright in his own bed which was right next to Nezuko's, he looked at her with wide eyes, disbelief partially filling his expression, "Hey, you're awake." Zenitsu said.

"W-What!? Where is Onii-chan?!" she cried out in return, "You mean Tanjiro? I don't know, they probably put him in another room considering he's a Demon, but I never heard them mention taking in a Demon.", Nezuko felt her heart sink deep into her stomach, she wasn't able to protect Tanjiro in the end, last thing she remembered was rage consuming her before she was knocked out cold by the Demon she was supposed to kill, a member of the Twelve Kizuki, that meant Tanjiro was probably still on that mountain, unless they already cleared it out in which case Tanjiro was most certainly already dead.

Nezuko wanted to believe in the former, that Tanjiro was still alive, Tanjiro could handle himself right? She hoped...
Soon after, Nezuko realized the present snoring, turning to her left and seeing some guy wearing a boar mask, "U-Uhm, Zenitsu? Do you know who that is?" she asked, Zenitsu pondered for a bit before he came with all he knew, "I saw him come flying out of that weird Tsuzumi house at one point, he tried to leave the scene but fell into some bushes and was out cold for hours, he didn't even twitch while he laid there, I thought he had somehow died so I never bothered to check up on him. Apparently he came to Natagumo Mountain too and sustained a few nasty injuries fighting some of the Demons there. The Kakushi found him suspended upside-down hanging from a tree half wrapped up in a cocoon, he was screaming at the top of his lungs and remained that way until he was subdued here."

"The Kakushi?"

"They're the people that clean up after Demon Slayers, they consist mainly of people with no swordsman skills, my Gramps taught me about them."

"O-Oh. Wait, do you think they might've collected Onii-chan?"

"I don't knooow, why aren't you concerned about me!?"

"Well, because from what I can see you're in decently good shape." Nezuko said before she let out a giggle, initially Zenitsu looked like he was ready to burst steam before he shook his head and crossed his arms, stubbornly looking out infront of him as to avoid conversation, that was when Nezuko noticed his arms, "Zenitsu? What happened to your arms…?", Zenitsu flinched for a bit before he slowly turned to face Nezuko again and began flailing his little arms about, "I got bitten by this weird spider-thing and I almost got turned into a spider myself because of it, so my limbs are really short right now." he half-cried out before someone that looked like she worked here quickly approached him, "And that's why you need to take your medicine!" she said, Zenitsu screamed from the sudden interaction and when he turned to face the person he just kept crying, "But it tastes so baaaad! Do I really have to take it five times a day!?", the girl quickly confirmed it by saying "Yes, five times a day."

Nezuko decided to pay more attention to the other Demon Slayer in the room, boar-man, while Zenitsu cried on in the background, "Excuse me, but who is that?" she asked, the girl that was 'bothering' Zenitsu looked over to see who Nezuko was referring to, "Oh, that's Hashibira Inosuke, from what I can tell it looks like he was raised by wild animals or something, he kept yelling at the Kakushi to unhand him so he could fight them, but it didn't make much of an impression with his hoarse voice."

"I see… Actually, do you mind telling me where I am, exactly? Last thing I remember is fighting on the mountain and now I'm here."

"Oh, this is the Butterfly Estate, it serves as part of Headquarters, a hospital, and the home of one of the Hashiras. I'm one of the people that work here, you can call me Aoi."

"Ah…"

"Speaking of hospitals, would you keep it quiet?! This is a Hospital Ward!" Aoi said firmly to Zenitsu, who only screamed louder before settling in his bed with clacking teeth, "I swear, this guy is totally not fit to be a Demon Slayer if he acts like this."

Nezuko smiled slightly at Zenitsu's antics, she was glad atleast he was okay, but now that someone who worked here was present she might aswell ask the big question, "U-Uhm, did you happen to also pick up a Demon Slayer with a green checkered Haori? He's my older brother, you see.", Aoi quickly shot up and seemed to be in thought, before she just shook her head, "Nope, sorry, must've died on the mountain before help could arrive.", Nezuko's mood dipped further, "My condolences." she continued.

Needless to say Nezuko's mood was extremely sour while she was recovering, every day Zenitsu would ask her what was wrong, but she'd remain silent.

One of these days, she had a visitor, it was that Slayer on the mountain he had encountered, the one that got so angry about the number of Mizunotos, he approached Nezuko's bed with a stool and sat down on it, the two stared at each other for a short while before Nezuko just began, "Uh, h-hey. You're that Demon Slayer from the mountain, right?", "Yeah, I owe you a bit for helping me back there, I don't think we ever introduced ourselves right?" the Slayer answered, "You can just call me Murata." he said, "Ah! Nice to meet you, I'm Nezuko, Kamado Nezuko."

Murata scanned the room for a bit, before looking at Nezuko again, "Say, where's that other Slayer that was with you?", Nezuko's mood dipped again, "He's my older brother, apparently he didn't make it..."

"O-Oh! Sorry… Anyways, I came to see you because I heard you survived the whole ordeal. Lucky you, getting to recover in a bed like this. I was brought to the Hashira Meeting to do a detailed report on the whole incident, apparently many of the Demon Slayers on the mountain didn't follow orders, they also said the Corps was declining in quality and they wanted to know who keeps training so-called 'lackeys'. To make matters worse they keep sending Demon Slayers to the mountain to scout things out, I'm supposed to go back there tomorrow... It was hell! Those Hashira are terrifying!", during his time of complaining Murata completely failed to notice one of said Hashira approaching him, "Hello!" she said, before Murata quickly got up, "Hashira! Lady Kocho!"

"Hello."

"Hello! Goodbye!", and Murata went off, quickly shutting the door behind him, through his drumming footsteps Kocho didn't know whether to say goodbye aswell, before she just decided to do so anyways, "Oh my, oh my. Goodbye." she said before turning her attention to the patients, "How are you all feelings?" she said with a smile, "I'm feeling better, thanks for asking." Nezuko said, Inosuke jumped up from his bed, clearly showing he too was ready, "You! Fight me!" he just said before Kocho walked over and quietly settled him back down in his bed, Inosuke didn't bother to respond while he looked at her smile.

"Then let's have you start your rehabilitation training, shall we?" Kocho said, "Rehabilitation Training?" Nezuko asked.

"Correct! You've all been bedridden for a month now and that'll only make your joints stiff, so every Demon Slayer goes through Rehabilitation Training after recovery to make sure they're back in tip-top condition!"

. . .

"The sounds that Shinobu makes are really unique, I've never heard anything like them before. They're so weird it's kinda scary." Zenitsu thought to himself as he examined himself through a mirror, specifically his hair that was falling out previously, "But she was like a goddess when she healed the people that became spiders, no wonder they flocked to her in tears. She's really pretty too, I bet she can make a living off of her looks alone. For about a week now she's been taking that boar-head and Nezuko to something called 'Rehabilitation Training', any moment now they'll come back…", before Zenitsu finished his sentence the door slid open, and out came the two other Demon Slayers looking like they were ready to die, both of them crawled in their respective beds and turned away from Zenitsu, "...Looking like that! It's scary!"
"H-Hey, Nezuko-chan? What happened?" he asked, but all he got was a 'sorry' from under her breath, Inosuke, the supposedly loud-mouthed monster he was, remained silent entirely, it scared him out of his mind, "Aaaagh! Come on! I'm going to be joining you tomorrow and I really don't want to die!" he cried out.

The next day, Zenitsu stammered behind the others, tugging Nezuko's clothes while whining to himself mentally, he didn't want to go, but he had no choice in the matter.
Once in the training room, the three sat down on the ground as Aoi began to explain, "Zenitsu, since it's your first day I'll explain everything again. First over there." she said, pointing to a group of triples hovering over a laid-out Futon, "...You'll lie down and those girls will loosen up your stiff muscles. Then reflex training." she continued as she pointed to a table, on it stood a series of cups, and by the table sat someone that looked a bit familiar to Nezuko, "Each of these cups contains medicated water, you'll be competing to see who takes it, your objective is to splash your opponent, but if your opponent blocks the cup you were about to use you must put it back down. Lastly, full body training, in simpler terms you'll be playing tag, your opponents are me and Kanao over here."

A gloomy aura filled the three patients waiting to be trained, before Zenitsu spoke up, "Excuse me, may we have a moment?"

"Hm? Do you have a question?" Aoi asked, "No… It's just, you, boar-head, come over here."

"Nope." Inosuke replied.

"I SAID COME OVER HERE!", before Inosuke even had a second chance to reply he was dragged out of the room, screaming soon followed outside before a loud thwack sound, followed by more screaming.
Eventually the two came back inside and Zenitsu looked like he was in heaven, training soon began and Zenitsu's smile only brightened, much to Nezuko's horror.

Inosuke's and Nezuko's training remained the same painful marathon, but atleast Inosuke seemed a bit more motivated.

It had been a month since he was forced to join the Spider Family, and Tanjiro realized just why the supposed Mother yearned for death, the family was not a family at all and it felt horrible to be a part of them.
Almost every day he'd get punished by the patriarch of the family, he'd learned his name by now, Rui.
Supposedly he didn't meet Rui's expectations as a 'Big Brother', Tanjiro hated being called 'Big Brother' by Rui.
When he was first forced, they made him drink a cocktail containing some of Rui's blood, the transformation was painful, made worse by Rui piercing several places of Tanjiro's body with his fingers, the result?

His body had gone pale entirely, his hair was white too and had returned to its long strands, so he had to keep them in a bun again, his sclera had gone blood-red while his irises were a pale blue, his pupils looked like those of the rest of the spider family and the weird maroon flame on his head had become a web of red dots and lines that roughly mimicked its original shape, those same lines were present on his arms too.
He had also been forced to wear a Kimono much to Rui's own, he looked like a bonafide member of the Family, he hated every bit of it.

Luckily, his usual accessories were kept around and he was allowed to keep his sword on his waist, Rui had already figured he'd only hold Tanjiro's abilities back if he couldn't fight with a sword, they never took his Hanafuda earrings and he knew where they had kept his Haori, which he would wear when alone, it made him feel like that in a sense he was still close to his sister.

Apparently the family had already cut a lot of losses, all that were left was Rui, himself, two younger siblings, and the Father.
Tanjiro got along decently with his new 'younger sister', she reminded him somewhat of Hanako and it was clear she didn't like being part of the family either, the 'younger brother' was a completely different story however and the two didn't get along in the slightest, he didn't know what the younger sister did, but the younger brother's job was to create the spiders that littered the mountain, he didn't know how he made them just yet, but he probably didn't want to know.
Though, Tanjiro could feel the presence of the spiders, like he had some kind of bond, if he focused hard enough he could even peek through their eyes for a brief moment which is probably how Rui kept an eye on the mountain.

If there were positives in becoming a member, it was that his speech somewhat returned to him, although he was stuttery sometimes and some words were just impossible for him, and the fact he could weave threads like most of the other members of the family, granted his threads were by far not as strong as Rui's and were far less capable of cutting, but they were sturdy and couldn't be cut easily, supposedly most of the family members had a unique alteration to the thread technique and his was nets, so it was his job to go out and set traps at night.

Whenever he'd get the chance, he'd silently free whoever got caught in his traps, and he pitied those that he had no chance to save.
Those that were killed were presented each day as a meal, Tanjiro initially didn't eat, it made the punishments he got worse, so since a few days he had actually began to eat with the family and it made him feel terrible about himself, he felt terrible his body relished the taste of human flesh and blood and he felt terrible Nezuko would probably have to kill herself for this.

This particular night he had perched himself up on a rock, watching the river flow by, tonight he had decided not to wear his Haori.

He was lucky he hadn't, while he was looking at the river he heard the bushes move behind him, and then a familiar voice spoke out, "Big Brother." they said, it made Tanjiro want to puke, it was Rui.
Tanjiro turned around to face him, the two stared at each other in silence for a bit before Rui continued, "Big Brother, You're still thinking about her right? Don't worry, she's still alive and I don't think she's stupid enough to come back for you. You're a member of our family now remember? So play your role properly. I have high hopes for you and I'd rather not string you up until dawn, for now.", Tanjiro just nodded absent-mindedly, Rui didn't really seem like he was expecting an answer and left Tanjiro alone again.

To his knowledge, there were so many wounded on the mountain that they had to abort the mission, every now and then they'd still send scouts to the mountain who would flee at the first sign of danger, he'd sometimes overhear them talking and from what he could gather they were planning on performing a proper raid on the mountain now that it had been revealed a member of the Twelve Kizuki was present here.
It made Tanjiro a bit happier knowing that they were still planning to wipe out this pretend-family, but that raised the possibility of him being identified as a regular member and killed without mercy.

He could feel another one of his traps snapping shut, so he got up and went over to inspect its supposed 'catch'.
What confronted him once he got there was actually a quite shocking scene, his eyes widened as he recognized the Slayer's bland black features, watching the Slayer try to slice his net, failing miserably in the process.
Tanjiro sprinted over to him, and after the two made eye contact Tanjiro began to break the net apart, for him severing his own threads was an incredibly easy job afterall, and afterwards he ushered the Slayer to stand up.
"Uhm, thanks?" he said, "You're just going to kill me now, aren't you?"

"N-No!" Tanjiro found himself stammering, "What?! Aren't you part of this supposed Spider Family?!" the Slayer asked in return.

Tanjiro somberly nodded, "The family is… Not a real family… I h-hate being pa-part of it." he said under his breath, "I want… To be with Nezuko…"

"WAIT, YOU MEAN… YOU'RE HER OLDER BROTHER!?", Tanjiro had to shush the Slayer, he didn't want to attract any unwanted attention afterall, Rui would definitely kill him if he found out he was freeing Slayers, Tanjiro could feel one of the spiders approaching so he ushered for the Slayer to leave, who decided that getting out of this alive was a better idea than getting eaten by a family of Spider Demons, so he bowed and ran.

Suddenly it was only Nezuko who came to rehabilitation training, both Zenitsu and Inosuke had stopped coming all together one day, she tried to get them to come along but failed miserably in the process, "Sorry." she said as she bowed her head to Aoi, "Just you!? I can't believe those two!" Aoi responded before training began again.

"I'll work hard for us all! Then I'll teach them how to win!" Nezuko thought as she lost ten more times and was allowed back to the hospital ward, while walking she kept pondering to herself, considering Kanao was so much stronger than all of them, "Why is she so much stronger? What's the difference? Her reflexes are on a totally different level, I'd probably still lose on my best day.", she completely missed the three little voices calling her name while she was deep in thought, before she felt a tug on her arm and looked down, there the triplets stood, they looked worried, "Are you alright, Nezuko?" one asked, "A-Ah! Yeah I'm fine, I was just deep in thought." she said, "What is it?" she asked after.
The triplets murmured amongst each other before one of them handed her a towel, "Uhm, here, a towel." she said, "Oh! A towel! How kind!" Nezuko responded as she gratefully took the towel and began drying herself off, the triplets beamed with joy from her response.

"Uhm, Nezuko? Do you maintain Total Concentration Breathing all around the clock?" one of the triplets asked, Nezuko was stumped, around the clock? So they continued, "You know, dawn, noon, night, even while sleeping?"

"No, I don't… Is that even possible?"

"Yeah! Doing that makes a world of difference!"

"It's pretty hard using Total Concentration Breathing even a little, so the whole day…"

"Some people are able to do it! Like the Hashira! Even Kanao! You should try!"

"Great idea! I'm giving it a try! Thank you!"

. . .

Great idea? Yeah right. Nezuko had been trying it and she felt like her chest was about to rupture entirely, her entire body was covered in sweat from trying, "W-What was that!?" she suddenly said to herself, before she smacked the sides of her head firmly, "I-I… I thought my heart was going to come out of my ears…! Aaaagh! This is too hard!"
"...Breathing starts with the lungs, if my lungs are bad, I'll just have to start there! I'll get up early and do some laps! Then I'll hold my breath! If I just keep that up I'll be able to maintain Total Concentration Breathing all day." she thought, before screaming to herself to give herself some encouragement.

. . .

"Blow into these gourds?" Nezuko asked while eating an Onigiri, the triplets had just presented a few gourds to her, "Yes! When Shinobu was training Kanao, she often made her blow into these gourds."

"Oh! That's an interesting training, does it make a sound?"

"No, you're supposed to blow them up!"

"Oh!" Nezuko said happily before realization struck her, "Oh..."
"Huh!? Me!? Blow this up!? A dried Gourd!?"

"Uh-huh! And these are special Gourds, they're even harder than normal ones...!"

"Kanao blew them up!? By blowing into them!?"

"...And as she was training, the gourds got bigger and bigger, right now she's working on…" Thud, the other two of the triplets had gone and gotten a massive Gourd, almost the size of Nezuko herself, "...This gourd!"

"THAT'S… HUGE! I GOTTA TRY!"

Fifteen days passed like that.
Nezuko had been putting herself through her own hellish training, she wanted to be stronger, she wanted to be stronger for Tanjiro, every night she'd sit on top of the Butterfly Estate and practice her breathing.
"Good, my strength is coming back. I can run more than before, and my lungs have gotten stronger, so this is good.", she wanted to rush, but she knew she couldn't, it partially infuriated her, "During the day, I train myself by moving around alot with fast movements, now it's time for me to breathe slowly and deeply circulate air all the way to my fingertips. Meditation improves concentration, Urokodaki said that. Urokodaki said-" Nezuko's thoughts wandered off to Haganezuka probably already being absolutely livid about her sword being broken.
"Sorry…" she thought to herself, her mind wandered off again, this time thinking about the possibilities of what could've happened after she passed out on the mountain, she flinched when she imagined Tanjiro decapitated and crumbling to dust before her.
She completely missed the woman greeting her a few times over, before the final "Hello there!" snapped her back to reality, Nezuko looked over to the source and immediately came eye to eye with Shinobu whom was sitting uncomfortably close to her, "You're really dedicated." she said, "Your two friends ran off somewhere, aren't you lonely all by yourself?"

"Nope!" Nezuko yelled out with vigor, "Once I can do it, I'll teach them too! Besides… my Brother is with me in spirit!"

"You have a pure heart." Shinobu said, followed by an extended silence, before Nezuko broke the silence, "Uhm…" she began, "Why'd you bring us here…?"

"Because I'm already aware of your brother.", Nezuko flinched, does that mean the other Hashira know too? "Plus, your injuries were plain horrible. Also, I thought I could entrust my dream to you."

"Dream?"

"My dream of getting along with Demons, I'm sure you can achieve that."

"...Wow! I never expected a Hashira to have that kind of dream… From what I heard you guys can be pretty scary…"

"Well, It's not per-se my dream, it was that of my Elder Sister, I decided to inherit it after a Demon killed her… Even when she was dying she pitied the Demon responsible for her death, but I don't know if I can keep that dream up much longer, hence why I'm entrusting it to you!"

"O-Oh… I see… I'll do my best!", before Nezuko had finished her sentence Shinobu had disappeared, leaving Nezuko alone again.

. . .

"Naho! Kiyu! Sumi!" I want you to help me train!" Nezuko said to the Butterfly Estate's triplets, "When I'm asleep, if I stop doing concentration breathing, hit my covers with these blanket beaters!" she said while holding a pair of said blanket beaters, the triplets stared back at her for a few seconds, before they responded with a loud "You got it!", Nezuko thanked them profusely while bowing.
That night, while Nezuko was firmly asleep, the trio waited beside her, each holding a blanket beater in hand and waiting for the right moment, initially it went smoothly as Nezuko's breathing didn't falter during sleep, until her snoring broke through the tranquil moment and she was beaten awake, this continued for several days.

By the tenth day, Nezuko once more tried to blow into a Gourd, which by now was half her size, she took a deep breath and blew, allowing her lungs to go full overdrive while the triplets cheered her on, eventually the Gourd blew apart, leaving the four to celebrate.
When she partook in Rehabilitation Training after she could definitely see the difference, during Full Body Training she was able to beat Kanao, and during Reflex Training the arms of the two girls viciously flung across the table, blocking each others cups until Nezuko broke through Kanao's defences, and finally drenched her in the medicated water, the triplets broke out in a victory cheer soon joined by Nezuko, they hadn't picked up on the either Inosuke or Zenitsu staring at them through the open doorway, stumped.