One possible reason could be that Dudley has finally grown up and realized how mean he has been to Harry all these years. Maybe he had an experience that made him see the error of his ways, like facing real danger himself and seeing Harry's bravery in a new light.
Harry might be initially skeptical. After all the years of torment from Dudley, he can't just immediately trust this change. But if he sees that Dudley is truly sincere, he could accept the apology with grace.
Harry might become more open and less guarded. Since he now has a brother in Dudley, he might feel more at home in the Muggle world. Dudley, on the other hand, could become less of a bully. The knowledge that he has a wizard for a brother could make him more humble and empathetic.
Well, Harry and Dudley's relationship would change drastically. Harry, by adopting Dudley's child, is taking on a huge responsibility. Dudley might initially be in denial about the whole situation, but as time passes, he realizes that Harry is providing a better life for his offspring. This could lead to a thaw in their long - standing animosity. Harry might start to view Dudley as someone who has made mistakes but is also trying to do right by his child in his own way. And Dudley could start to view Harry as a real family member, someone he can rely on.
It could be that Dudley has his own reasons to oppose the dark forces that are after Harry. He might see that if Harry fails, it could also mean trouble for him and his family. So, he decides to train Harry to fight as a way of self - preservation as well as helping Harry. Another reason could be that Dudley has grown to respect Harry over time and wants to contribute to Harry's ability to defend himself against the many threats he faces.
Sure. Fanfiction often takes the existing characters and situations and twists them. For Harry and Dudley, it could start with a shared experience that makes Dudley realize Harry isn't so bad. Maybe they get caught up in a magical adventure together outside of the normal Hogwarts - related stuff. This common experience could break down the barriers between them and start a friendship.
Well, if Harry and Dudley became friends, it would drastically change the whole dynamic of the early Harry Potter story. For one, Harry might not have felt so alone at the Dursleys' place. Dudley could have protected Harry from Vernon's wrath. Also, they could have shared secrets about the wizarding world with Dudley being a Muggle. This new friendship might even have led to Dudley developing an understanding and acceptance of the magical world much earlier, and perhaps he could have been an ally to Harry in the fight against Voldemort, instead of a bully.
In this fanfiction, perhaps Dudley's envy of Harry's magical world finally boiled over into uncontrollable rage. He might have found a way to cross into the wizarding world without anyone knowing. And in a moment of extreme jealousy and anger, Dudley could have used some kind of weapon or spell (maybe through some dark magic loophole) against Harry, which unfortunately led to Harry's death. Fanfiction allows for these extreme and unexpected plot twists.
Harry could become more relaxed. After all the battles and traumas of his youth, as an adult he might be more at peace. He could be less impulsive and more calculating. Dudley, having matured, might lose his bullying nature completely. He could be more empathetic, especially after experiencing some hardships in his own life that made him realize how his actions affected others.
It could completely transform their relationship. If they have a positive reunion, they might become friends. They could start to support each other in different ways. Harry could use his magic skills to help Dudley out in small ways, like fixing something around his house without Dudley knowing it was magic. Dudley, in return, could offer Harry some insights into the Muggle world that Harry might not be fully aware of.
Well, one possible plot could be that Dudley gets into some kind of trouble or situation where he can't take care of his child. Harry, having grown into a kind and responsible person, steps in. He might introduce the child to the wizarding world in a gentle way, teaching the kid about magic and also about the importance of family values. The story could also involve the child struggling to fit in both the Muggle and wizarding worlds, with Harry as their guide.