His relationship might develop with a lot of forgiveness. If his father is part of the family reunion, Luke may have to forgive his past wrongdoings. They could start to train together, strengthening their bond through the sharing of Jedi knowledge.
Well, it depends on how the fanfiction is written. He could meet his family in a completely different setting. Maybe they are all in a peaceful place that is far from the wars. His family might teach him new Jedi skills or knowledge that he didn't have before, which would make him even more powerful.
It could make him more empathetic. Interacting with his family, he would understand different perspectives. If his mother tells him about her political struggles, he would see a different side of the galaxy's problems. This new understanding would shape how he approaches future challenges in the Rebellion. He may start to consider diplomatic solutions more often rather than just relying on his lightsaber.
In this kind of fanfiction, Luke might have an emotional reunion with his family. He could finally have a long talk with his father, Anakin, about the past and redemption. Maybe he'd share his adventures with his mother, Padmé, if she were somehow brought back in the fanfic's alternate reality.
As they go on adventures together, their bond would strengthen. They could face a great enemy like a powerful dark side user. In the heat of battle, they would rely on each other and start to trust more deeply. Ahsoka might see some of Anakin in Luke, which would make her more protective of him, and Luke would see Ahsoka as a wise mentor figure.
In many such fanfictions, their relationship becomes more positive. Vader starts to see Luke as a chance for true redemption. He may become more of a mentor to Luke, sharing his knowledge of the Force.
The relationship could develop in a complex way. Since Vader has captured Luke, there's a power imbalance. However, as they interact, Luke might try to reach out to the good in Vader. Vader, in turn, might be conflicted. He could start to protect Luke from the Emperor's harsher plans, leading to a strange alliance within the captivity.
In fanfiction, their relationship could develop more quickly towards mutual understanding. Maybe Luke could convince Vader to turn away from the dark side much earlier, and they could start training together as Jedi. This would be a huge shift from the original story.
His character would develop in a very different direction. He'd be more independent and self - reliant. No longer bound by the strict Jedi code, he could explore the darker aspects of his personality. He might become more cynical and worldly. His skills with a lightsaber could be used more for intimidation and self - defense in the cutthroat pirate world. His view of the Force might also change, seeing it as a tool to gain power and wealth rather than just a spiritual guide.
Luke's character would develop a darker side, not in terms of being evil, but in having to face the inner turmoil of his vampiric existence. He'd have to constantly fight the urge to feed, which could make him more empathetic towards those who struggle with their own inner demons. His relationships with other characters would change significantly. Han and Leia might be hesitant to trust him at first, but as he proves himself, they'd come to accept him again. His physical abilities would also change, and he'd have to adapt his fighting style to his new vampire - enhanced strength and speed.
He might feel conflicted. On one hand, there could be a part of him that is intrigued by the power and influence that comes with being Vader's heir. But on the other hand, his loyalty to the Rebel cause and his Jedi ideals would be pulling him in the opposite direction. He may struggle with whether he can use this new position to bring about positive change in the Empire or if he should reject it outright.