Arya's story arc would change in multiple ways. First, her identity as a Stark would take on new meaning. With Rhaegar winning, the North's relationship with the Iron Throne is different. Arya may be used as a pawn in the political games between Rhaegar and the North. Second, her training as a faceless man might be used for Rhaegar's purposes. He could send her on secret missions, which would change her focus from personal revenge to serving the new king. Also, her view of the world would change. Instead of seeing the world in terms of good and bad (her enemies and those she wants to protect), she'd have to see it in terms of political allies and enemies under Rhaegar's rule.
If Rhaegar wins in the fanfic, Arya Stark's story arc would change drastically. Arya is a character defined by her quest for justice and revenge in the original story. But with Rhaegar in power, she may find herself in a different kind of fight. She could be drawn into the power struggle between Rhaegar and other potential claimants to the throne. Her skills as a faceless man would be valuable in this new political arena. She might also have to deal with the new social order that Rhaegar would establish. Her relationships with other characters would also be different. For instance, she may form an alliance with some of Rhaegar's supporters or be at odds with those who oppose his rule. This would all reshape her journey from a lone avenger to a key player in a complex political drama.
Well, if Rhaegar wins in this fanfic, Arya Stark could be a sort of diplomat for the North. Rhaegar would need to keep the North in line, and Arya, being a Stark, has the influence to do that. She might also befriend Rhaegar's family, like his sister or wife if he has one. Her journey could change from seeking revenge to building a new world under Rhaegar's rule. Maybe she'd even teach some of Rhaegar's men her unique skills, making them better fighters and spies.
The characters' fates would be drastically different. Daenerys might not have to go through all the hardships she faced in the original story as she could grow up in a more stable Targaryen - ruled Westeros. Tyrion could find himself in a court that values intelligence more, given Rhaegar's own intellectual pursuits.
If Rhaegar won in the 'Game of Thrones' fanfic, perhaps the Targaryen dynasty would be restored to its former glory. He might bring about a more just rule, with less bloodshed compared to the chaotic events that unfold in the original series. He could also potentially reunite the Seven Kingdoms under one banner more peacefully, using his charm and leadership skills.
It would make her more confident. Having a dragon gives her a huge power advantage, and she would no longer have to rely solely on her assassin skills. This newfound power could make her bolder in her actions and decisions.
It would likely make her more powerful and feared. Having a dragon gives her a huge advantage in battles and in political power plays. Her character might become more confident and assertive, as she now has a great weapon at her disposal. She could use the dragon to exact revenge on her enemies more swiftly and decisively.
If Rhaegar were to win in a 'Game of Thrones' fanfic, it would change the fates of many characters. For example, Ned Stark's life would be different. He wouldn't be on a quest for revenge against the Targaryens for his sister's supposed abduction. Instead, he might be serving under Rhaegar in some capacity, perhaps as an advisor or a military leader in the North. The Lannisters would also have to re - evaluate their position. Their plans for power might be thwarted as Rhaegar would be in control. Jaime Lannister might not become the Kingslayer in the same way, and Cersei's ambitions for the throne would be dashed. Overall, the power dynamics in Westeros would be completely reshaped with Rhaegar's victory.
If Rhaegar won in a 'Game of Thrones' fanfic, perhaps he could have restored the Targaryen dynasty to its former glory. He might have been able to bring about a more peaceful reign, with his love for music and the arts influencing the court. He could also have made different alliances, changing the political landscape of Westeros completely.
Arya's identity as a Stark would be more deeply ingrained in her. She would start to embrace all the values that the Starks stand for. She might even try to teach these values to the people of the North. Her development would also involve her coming to terms with her past as a Faceless Man. She would decide how much of that part of her should be part of the new Stark legacy she is building.
Well, it would change a great deal. Arya is a skilled assassin. With a dragon, she would have a powerful weapon at her disposal. She could use the dragon to quickly travel across Westeros and surprise her enemies. Her revenge list might get shorter very fast as she could just burn down the castles of those who wronged her family. For example, she could easily take on the Boltons at Winterfell if she had a dragon by her side.
Often, you'll find themes of redemption and change. Since Rhaegar's actions had such a big impact on the overall story of 'Game of Thrones', some fanfictions use his relationship with Arya to show a different path for him. And for Arya, it can be about finding love in an unexpected place. There's also the theme of power dynamics, as Rhaegar was from a more noble and powerful background compared to Arya who had to fight for her place.