Welcome back!
I am aware that judging by the map, meeting in Brookbridge (which I have located somewhere between the Goldroad and Silverhill) is strategically not the smartest place.
Bucky has to pass through King's Landing via the King's Road and he could have met his sister at Crossroad's Inn. However, in my canon he wants to visit Steve and so does Nat and therefore they make their way down.
It makes more sense for Peggy though as she is on the way to Casterly Rock and there aren't so many keeps close to the Goldroad.

The GoT timelines differ according to where you look therefore I decided to go with the tourney at 279 A.C. and go from there. Rhaenys is born in early 280 A.C.

Disclaimer: I neither own Marvel nor GOT.

Goldroad, 280 A.C.

Margaery (Peggy)

The terrain was getting more hilly by the day they were riding towards the West, it was quite interesting actually, but Peggy was getting tired. Tired of the chatting of the people around her, tired of the stale food they served at the inns, even the more expensive ones, and tired of riding all day. She was more and more looking forward to Brookbridge and meeting the people there, yes, she really was curious. But most of all it would be great to have some days of rest, a soft bed and a long, hot bath. Sure, she could sit in one of the carriages like her ladies-in-waiting for now, but being shaken through all day on the bumpy Goldroad sounded even less appealing than her chaffed legs from riding. At least sitting on her white zelter she could feel the crisp air with the faint smell of wildflowers. Even though she was a lady she was not using a side saddle, she found the mens' version far more practical and comfortable. As a consequence, her long dress and coat were altered with high slits on the sides so that they would still fall over the flanks of her horse and cover everything that should be covered to protect her modesty. While the dress was made only from light-green linnen it was still expensively decorated with embroidery of roses, befitting her house and status. It had long but unusually tight sleeves as she hated the volume of the fashionable trumpet sleeves to get in the way when riding or praticing fighting. Her coat was made from soft wool with sleeves that had been taken off for the moment, creating a kind of grey vest over the dress. If anything, Margaery Tyrell always looked special, she did not blend in unless she really wanted to.
Suddenly, she felt a shadow on her side, it was May, clothed all in black on her equally black stallion. Unless most of the other men in full plate armour, the exotic woman wore a lighter model that consisted of trousers and a long high-collared black coat over a silken shirt. Even though the sleeveless leather corset on top was embossed with metal details for further stability, it still made her more flexibel and quick. Her shoulders were only covered by the coat, but she had leather protections on her lower arms as was custom for people who were often handling bows. May thought helmets to be unnecessary when not confronting enemies on a traditional battlefield as they reduced her peripheral sight and dulled her ability to hear the tiniest sounds. Peggy could see that her hair had been intricately styled in several braids that were then connected with small ribbons, making her look even more special. The woman said nothing but her lady didn't mind, she was used to May's silence and often preferred it to the idle tattle of the other ladies.

It made her think back to the time in King's Landing that had just passed. Even though being in the capitol had been an adventure, she had been happy when they had left. Margaery was adept at politics already and had used the time to expand her connections even further, but that still did not mean she actually enjoyed what she had seen. The king was quite obviously going mad and the people's situation got worse and worse. Saying the wrong thing could get you killed in an instant, even if you were as rich and powerful as the Tyrells. They had stayed away from Court at their own private lodgings in the city which were far more peaceful than the Red Keep, and tried to avoid to have to meet Aerys. Of course, the key members of her party had still made their enquiries and gathered as much information as they could, all in their separate domains. While it had pained Peggy to see Elia in her current situation, hopeful but neglected by her husband, Tony had been so furious that it was nearly a miracle that he had not exploded and spoiled the whole visit. Realistically, Peggy knew that at the moment there was nothing she could do to help the princess, even though she would have liked to. However, it had also turned out that she had not given the Dornish lady enough credit when one night, Peggy's party had heard an urgend knock at their door and when a servant at opened, two cloaked figures had rushed in.

"Who are you and what is it that you want?" May hissed, appearing from the shadows, holding a knife to the taller figures neck.

The person, a man judging by the size, had simply held up his hands in surrender.

"We are only humble visitors, my lady" the title had been laced with mocking when the intruder, definitely a man by the voice, looked May up and down who was wearing men's clothing as usual.

The other person who was slimmer and currently seemd very much intimidated by Fury's cold stare if her frozen posture was any indication shifted the bundle in her arms and then flipped her hood back with one hand. Strands of chocolate brown hair tumbled forward, framing a young, beautiful face.

"Elia!" Tony, who had just come back from one of his latest expeditions to the King's Landing whorehouses, called, pulling her in an embrace.

"Watch out!" the Dornish woman called, just as the bundle started to wail. "Shush little one," she urgently started to shush the baby as Tony looked at her upset, apparently scared he had just crushed his niece. After a short while, the girl calmed down again.

"Well, it seems you have met Princess Rhaenys now, too," Elia's companion commented dryly.

Peggy started to study him intently. He was about her own age, had an incredibly handsome face, cheekbones you cut your fingers on and expressive eyes that somehow gave the impression they had seen to much already but also held quite a bit of mirth. The colour of his hair was hard to determine in the lamplight, but it was light, probably blonde. Even though it had been years since she had last seen him at a tourney, the woman was fairly certain that she knew whom she was talking to.

"Ser Jaime Lannister, I suppose," she stated.

"You are correct, Lady Margaery, I suppose," he answered in kind.

Peggy motioned for May to put down the knife which she did, but she didn't gratify Lannister with an answer.

"Your Highness, what brings you here at that time of day? It must be of some importance," Peggy started by adressing the prince's wife.

"I wanted to see my brother and to warn you."

Peggy raised an eyebrow and motioned towards the parlour. "Well, then you better have a seat. Would you care for anything to drink?"

"Some watered down wine would be nice, thank you," Elia answered politely while taking a seat on one of the chaises.

While a maid got the drinks, Tony settled down next to his half-sister who placed Rhaenys on his lap without further ado. Peggy nearly broke out in laughter when she saw his shocked face that slowly relaxed when he realized the baby wasn't going to explode anytime soon. Instead, the little girl only sucked her thumb, staring at the people around her. The Tyrell silently agreed with the people's judgement, she looked nothing like a Targaryen, but when her mother started talking about her husband, it was clear how helplessly in love the woman was. There was no way that little bundle was a bastard, Peggy was sure of that. Her Lannister guard stood close to the door, warily eying May who stood closer to her lady. The woman was silently amused when she noticed Fury lurking in the shadows.

"The king is truly mad!" Elia confirmed what they already knew, "and I doubt Rhaella will survive that much longer."

There was true regret in her voice, apparently she genuinely cared for the older woman.

"She tries to do what she can to shelter Viserys, but she can't be a real mother to him, she isn't even allowed to be alone with him! There is always a Kingsguard with him, no offence Ser Jaime. I hate to say it but I am so afraid this will spoil his character. And my little Rhaenys might have to marry him!" she nearly sobbed. "I can only hope for a son to continue the line and to spare the child the prospect of marrying Viserys!"

Peggy considered for a moment. "Don't despair yet, my princess. There might be other options. Think about all the marriages about to happen. Brandon Stark and Catelyn Tully, their son will be heir of the North. Lyanna Stark and Robert Baratheon, their son will inherit Storm's End. My nephew Willas Tyerell will one day be Warden of the South. So you see, there are plenty of good matches. Also, no offence to the two of you -" she motioned at Elia and Tony, "but you have two brothers who are both foolish in their own ways."

When Tony wanted to speak up, she raised her hand, silencing him.

"You know I am right. Oberyn is a smart, skilled man who will travel the world and do great things, but he is hot-tempered and irrational. He is a warrior and not a ruler, so we can only hope he either never becomes ruling prince of Dorne or marries a smart woman who can handle him. And who accepts his offspring. How many are there now? Three? Four? And Doran is a good ruler, a good man, but he really thinks it is a good idea to plot to marry his precious Arianne to Viserys. Of course she would become queen, but at what price? Still, if she does, it would also disqualify Rhaenys."

There was silence for a moment, before Elia spoke up.

"Maybe you are right Lady Margaery, but you think you know everything. Do you know what price you are going to pay when you marry Stannis Baratheon? I am not only talking about the man, but you will have Robert Baratheon as your brother-in-law, together with Lady Lyanna."

"Forgive me your Highness, but you sound jealous," Peggy remarked dryly, "it doesn't do you any favours but only makes you appear sullen and bitter. Not that I can't relate, I totally understand what you are saying," she added with more empathy. "If it gives you any peace of mind, I am certain Robert Baratheon will father nearly as many bastards as Prince Oberyn despite marrying the so declared love of his life. I quite enjoy Lady Lyanna, actually, from the few interactions we have had. Also, I am fully aware what kind of man I am marrying."

Peggy wasn't just a pawn in this game, she was a player, and she figured Elia should slowly start to understand this.

"Then there is only one last thing to tell you Lady Margaery," she said a bit coldly, "though you probably also know that, too. The King has taken a mistress besides the Queen."

Margaery nodded, not sure where this was going.

"I believe she is not yet but at the speed he is raping her, she will be with child soon. I don't know what they will do to her then. I don't know what they will do to her in any case. There has been talk..." Elia stopped, looking at the other lady intently, her eyes so similar to her brothers', "there has been talk that you know how to protect people. I know your mother plays it like a game, that is well-known. But I thought - no... forgive me, forget it."

She started to get up, but Peggy was quicker pushing her back and crouching down in front of her.

"What is it you ask of me, Your Highness?"

Elia swallowed.

"Can you save her?"

The Tyrell-woman shook her head.

"I have made my inquiries. She is guarded, more so than all of his treasures. I suppose we could get her out, but at a price I am not willing to pay. The King is mad Your Highness, we both know this, he might start a war and thousands might die! I am sorry, I thought this through and I really see no option."

Peggy didn't know what made her be honest with the dark-haired lady, it was treason what they were discussing, but here they were. Surprisingly, the princess only nodded, getting up and taking back her child.

"I don't know whether to hate or to admire you Lady Margaery. Maybe I do both," she said in parting, "either way, you are impressive. But I don't know whether you are a blessing or a curse to this world."

Her words had held something akin to a prophecy when she had disappeared into the night, her guard close to her after throwing her a look over his shoulder that she could not figure out. When they had been gone, she had asked Fury whether there was really no chance to rescue that woman. He had only shook his head.

Now, hundreds of miles away, the thoughts of her would still not let her alone.

May's armour is inspired by Tauriel's in "The Hobbit" but totally in black. The hairstyle is inspired by Ming Na Wen's in "The Mandalorian".
Also, drinking alcohol while being pregnant is bad for the child, but Elia doesn't know that.