This is how our group dealt with the stuff that happened after the breakout. I don't own it.
You like?

The isolated group at Headquarters have contact with the outside world.

The days slid by. Remus kept close to 12 Grimmauld Place, keeping Sirius company. This mostly involved making sure he didn't get too drunk and providing an ear for him to chew off through his moping. As well as looking for Kreacher — something odd was going on there, but Remus couldn't work out what. Of course, he played chess and solved crosswords with Dora when she was available.
The three enjoyed each other's company immensely.

Contact with the 'outside world', as Sirius termed it, was interesting. Something seemed to happen every month to shudder, laugh or gape about and comment on.

In March, it was Harry speaking out about what really happened last June. Dora had brought it in — after the article about Sirius in August, she'd taken out a subscription.
Anyway, Remus and Sirius had just played a chess match in the lounge when they heard the door open. Remus was only just in time to stop Dora from falling again. It was sort of funny, the amount of times this happened; she always seemed to forget where the troll-leg was. Not that Remus minded; it gave him an excuse to catch and hold her for a minute. Bad wolf! Don't go there! he thought crossly. Then he noticed the pallor of her face. "D-Tonks? What happened?"

She shivered. "You guys need to read this," she said heavily, holding out a copy of the Quibbler. The front was adorned with Harry's face, smiling sheepishly at the camera, accompanying the headline: "HARRY POTTER SPEAKS OUT AT LAST: THE TRUTH ABOUT HE-WHO-MUST-NOT-BE-NAMED
AND THE NIGHT I SAW HIM RETURN".
Sirius winced. "He's spoken out...? Whoa." he muttered, "Telling Dumbledore and I was hard enough, last year, but..."

They went into the kitchen. Remus got hot chocolate for everyone, then read the article, keeping an arm around Dora for comfort. The more Remus read, the sicker he felt. It was horrible.
"He's had to go through so much..." Dora mumbled, "I wonder if he's ever been a kid, really. No wonder he wants in on the Order stuff."
Remus sighed. "I know, Tonks, I know..."
Dora turned to Sirius. "By the way, I kinda told Mum about your innocence. She's always believed you were, but it just sort of slipped out while we talking about Trixy earlier today."
Sirius sighed. "About time. It was starting to annoy me."

The next major event happened in April, just before the Easter break.
Sirius, Remus and Dora were having a meal together when there was a sudden flash of silver and Minerva's Patronus materialised. "It has happened. The little Defence group we were informed about has been discovered... A less than willing member betrayed them and now sports a rather interesting collection of pimples — I believe they spell the word 'sneak'."
Dora and Sirius laughed. Remus smirked. "Hermione's doing, I suspect." he said.
Sirius added, "But — caught — are they -?"
The Patronus continued, "Were you aware they'd called themselves 'Dumbledore's Army'? I presume it had something to do with the fact that it's Cornelius' worst fear at the moment... At any rate, it
allowed Albus to take the blame."
Dora gasped. "They've forced him from Hogwarts?"

"He was forced from the school, but he had been planning for this eventuality. If it wasn't this, it would've been something else." The Patronus finished heavily.
Sirius snorted. "Idiot Fudge is only giving Voldemort more free rein." he grunted.
Remus was pleased to note Dora only jumped slightly at the name; his coaching was paying off. Then he was struck by an idea. "I wonder what Fred and George will make of this... After all, half the reason we tried to toe the line" — well, he had, anyway — "was because of Dumbledore..."
Sirius perked up. "And they can't be the only ones that do so..." he said slowly.
"Fudge has no idea of what he's unleashed, has he?" Dora said, with a smirk. The other two laughed.

A week or so after Easter, Sirius was upstairs, looking for Kreacher; he had disappeared again. Remus was downstairs reading dreadfully boring information about the Ministry and Death Eater activities (nothing but hints here and there; so damn frustrating) and wishing Dora was at Headquarters — she'd find some way to make the material interesting.
There was a sudden whoosh from the fireplace and then a voice said, "Sirius?"
Remus jumped and looked around. "Harry!" he said, feeling extremely shocked. "What are you - what's happened, is everything all right?"

"Yeah," said Harry. "I just wondered — I mean, I just fancied a – a chat with Sirius."
"I'll call him," said Remus, getting to his feet, still feeling perplexed, "he went upstairs to look for Kreacher, he seems to be hiding in the attic again…"
He ran upstairs and extracted Sirius from his mother's bedroom, where he was feeding Buckbeak. "I couldn't find him," he started to say, but Remus interrupted.
"Harry wants to talk to you. His head's in the fireplace."

Sirius gaped, then followed him downstairs. "What is it?" said Sirius urgently, sweeping his long dark hair out of his eyes and dropping to the ground in front of the fire, so that he and Harry were on a level. Remus knelt down too, feeling very concerned. What could've made Harry Floo-call Headquarters?
"Are you all right? Do you need help?" Sirius continued.

"No," said Harry, "it's nothing like that… I just wanted to talk… about my dad."

They exchanged a look of great surprise. What? Why?
Then, Harry started talking. "Okay, during an Occlumency lesson, Snape was called away and I was too curious for my own good I suppose..." he began, "I went into the Pensieve and saw what happened after your Defence O.W.L..."
Remus froze. Oh no. Of all the times it could have been...
When he had finished, neither Sirius nor Remus spoke for a moment. They were too stunned. Then Remus said quietly, "I wouldn't like you to judge your father on what you saw there, Harry. He was only fifteen -"

"I'm fifteen!" said Harry heatedly.
Yeah, bad argument...and – argh, he was sixteen by then, I thought of the Willow, not the Lake Incident. But I-I'm not correcting myself. That would just create more problems.
"Look, Harry," said Sirius placatingly, "James and Snape hated each other from the moment they set eyes on each other, it was just one of those things, you can understand that, can't you? I think James was everything Snape wanted to be — he was popular, he was good at Quidditch — good at pretty much everything. And Snape was just this little oddball who was up to his eyes in the Dark Arts, and James — whatever else he may have appeared to you, Harry — always hated the Dark Arts."
Remus wasn't entirely sure that was the whole reason they'd hated each other; at least, not after second year. But it was just suspicions and Remus wasn't going to be the one to tell that story. It wasn't his to tell, for one thing. And Sirius was glossing things over a bit, possibly. But if that's how he wanted to tell it…

Harry was speaking again. "Yeah, but he just attacked Snape for no good reason, just because — well, just because you said you were bored," he finished, with a slightly apologetic note in his voice. "I don't really want to blame you, but..." Harry was too good sometimes.
"I'm not proud of it," said Sirius quickly.

But how to explain what happened? Remus thought. He looked sideways at Sirius, then said, "Look, Harry, what you've got to understand is that your father and Sirius were the best in the school at whatever they did — everyone thought they were the height of cool — if they sometimes got a bit carried away -"

"If we were sometimes arrogant little berks, you mean," said Sirius.
Well, that's one way of putting it. Remus thought with a smile. But still…
"He kept messing up his hair," said Harry in a pained voice.
Sirius and Remus laughed. Oh, the memories...
"I'd forgotten he used to do that," said Sirius affectionately.
"Was he playing with the Snitch?" said Remus eagerly. He'd loved that...even if it was silly...

"Yeah," said Harry, looking on in puzzlement as Sirius and Remus beamed reminiscently. "Well… I thought he was a bit of an idiot." he said. Remus nearly laughed.
"Of course he was a bit of an idiot!" said Sirius bracingly, "we were all idiots! Well — not Moony so much," he said fairly, looking at Remus.

He's too kind. Remus shook his head. "Did I ever tell you to lay off Snape?" he said. "Did I ever have the guts to tell you I thought you were out of order?"
True, he had chewed them out afterwards, but...actually telling them off in front of the crowd? As if.

"Yeah, well," said Sirius, "you made us feel ashamed of ourselves sometimes… that was something…"
Remus sighed. He'd always been afraid of everyone — including Sirius and James — turning on him. After all, crowd mentality...

"And," said Harry doggedly, "he kept looking over at the girls by the lake, hoping they were watching him!"
"Oh, well, he always made a fool of himself whenever Lily was around," said Sirius, shrugging, "he couldn't stop himself showing off whenever he got near her."

"How come she married him?" Harry asked miserably. "She hated him!"
"Nah, she didn't," said Sirius.
"She started going out with him in seventh year," said Remus, lips twitching as he remembered how.
"Once James had deflated his head a bit," said Sirius.
"And stopped hexing people just for the fun of it," said Remus.

"Even Snape?" said Harry.
"Well," said Remus slowly, "Snape was a special case. I mean, he never lost an opportunity to curse James so you couldn't really expect James to take that lying down, could you?"
Part of the reason he'd formed the suspicions about their real rivalry in the first place... But – that's still not all of it. Yet I can't contradict Sirius now… after all, it would only lead to arguments. We need to be united, so we can explain, reassure… The words sounded somewhat hollow, even in his own ears.

"And my mum was okay with that?"
"She didn't know too much about it, to tell you the truth," said Sirius. "I mean, James didn't take Snape on dates with her and jinx him in front of her, did he?"
And she was terribly hurt by what Snape said when she did try to help that day...

Sirius frowned at Harry, who was still looking unconvinced. "Look," he said, "your father was the best friend I ever had and he was a good person. A lot of people are idiots at the age of fifteen. He grew out of it."
Remus nodded and smiled. It was in times like these that Sirius' insightful side came out. And, whatever else, that last part was (mostly) true – even if it took longer than Sirius perhaps remembered.

"Yeah, okay," said Harry heavily. "I just never thought I'd feel sorry for Snape."
"Now you mention it," said Remus, feeling tension between his eyebrows, "how did Snape react when he found you'd seen all this?" I can't believe I didn't ask sooner...he would've been furious...
"He told me he'd never teach me Occlumency again," said Harry indifferently, "like that's a big disappoint—"

"He WHAT?" shouted Sirius, causing Harry to jump and inhale a mouthful of ashes.
"Are you serious, Harry?" said Remus quickly. "He's stopped giving you lessons?"
This is not good...
"Yeah," said Harry, looking surprised. "But it's okay, I don't care, it's a bit of a relief to tell you the -"

"I'm coming up there to have a word with Snape!" said Sirius forcefully, and he actually made to stand up, but Remus wrenched him back down again.
"If anyone's going to tell Snape it will be me!" he said firmly. "But Harry, first of all, you're to go back to Snape and tell him that on no account is he to stop giving you lessons — when Dumbledore hears -"
"I can't tell him that, he'd kill me!" said Harry, outraged. "You didn't see him when we got out of the Pensieve."

"Harry there is nothing so important as you learning Occlumency!" said Remus sternly. "Do you understand me? Nothing!" Though I may see if I can talk to Albus... Harry really doesn't
sound happy. Then again, it's never that fun, learning Occlumency...
"Okay, okay," said Harry, sounding thoroughly annoyed. "I'll… I'll try and say something to him… but it won't be-"

He broke off, tilting his head as though listening. "Is that Kreacher coming downstairs?"
"No," said Sirius, glancing behind him. "It must be somebody your end."
Harry looked worried. "I'd better go!" he said hastily and pulled his head backwards out of the Grimmauld Place fire.
There was a long silence. Sirius sighed. "I wish he hadn't seen that."
Remus sighed. "I wish James could be here to explain it properly."
"Want a drink?" Sirius asked. Remus sighed. "Sure. We've earned one."
The rest of the afternoon was spent reminiscing about times gone by — happier times, when the Marauders were still whole.

Oh, Moony!
In this chapter, I tried to illustrate, again, Remus' conflicting interests.
The next chapter is a new one, thanks to Pottermore.