Harry might initially be in shock. He could feel a mix of anger and helplessness. Maybe he'd try to hold back his magic out of fear of getting into more trouble with Vernon.
Well, perhaps Vernon might beat Harry out of his extreme dislike for magic. He could be enraged by some accidental magic Harry does at home and lose his temper completely.
It might be a fan who was really intrigued by the relationship between Harry and Vernon and decided to take it to an extreme in their writing. There are so many fanfiction writers out there, some write for fun, some to explore different character dynamics. So, it could be anyone really.
Petunia could be a great addition. Her relationship with both Harry and Vernon adds a lot of complexity. She could be the mediator or the one causing more trouble between them, depending on the plot.
In some fanfictions, Harry might cope by finding solace in his friends at Hogwarts. He could talk to Hermione and Ron about what Vernon does, and their support gives him strength. For example, they might encourage him to focus on his magic studies as an escape from the Dursley's household.
Maybe Vernon is jealous of Harry's magical abilities. He might see Harry as a threat to his 'normal' family image. Also, Vernon has always been a bully at heart and Harry, being an easy target in his house, becomes the victim of his pent - up anger.
One common theme is redemption. Often, Vernon is depicted as having a chance to redeem himself for his past bad treatment of Harry. Another theme is the discovery of common ground. For example, they might find out they both have a love for a certain type of food or a shared fear. And family is also a theme. Despite their differences, they are still family in a way, and fanfictions sometimes explore how that family bond can be mended or redefined.
Perhaps Dudley finally stands up to his father's cruel treatment of Harry. Maybe he realizes that Vernon's behavior towards Harry is wrong and uses his own physical strength or some clever ruse to get Harry out of a difficult situation Vernon has put him in.
In some fanfiction, Uncle Vernon develops by becoming more accepting. For instance, he may start to see Harry not just as a freak but as a person with unique abilities that can be useful. He might begin to tolerate the wizarding world a bit more, especially if he realizes that Harry can use his magic to protect the family from certain threats.