Well, in these fanfictions, a frequent theme is the contrast between the Muggle world (represented by Vernon) and the wizarding world that Harry belongs to. Vernon's ignorance and fear of magic lead him to hurt Harry. Also, the theme of isolation is common. Vernon tries to isolate Harry from the wizarding world and his true identity, which causes a great deal of emotional pain for Harry. Moreover, there can be themes of revenge where Harry eventually gets back at Vernon for all the years of mistreatment once he gains more power and confidence in his magic.
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.
I'm not sure about specific 'vernon hurts harry' fanfiction off the top of my head. But you can try searching on fanfiction platforms like FanFiction.net or Archive of Our Own. Use the tags 'Vernon Dursley' and 'Harry Potter' and then look for stories where Vernon causes harm to Harry in the plot.
Often, there are plotlines where Harry uses his newfound knowledge from Hogwarts to outwit Vernon. He could use potions to make Vernon see things differently, or use charms to make his life at the Dursleys' more bearable. Also, some fanfictions might explore how Harry's relationship with the wizarding community as a whole helps him in his struggle against Vernon's hurtful behavior. For example, a kind wizard from the Ministry might step in to protect Harry after hearing about Vernon's actions.
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.
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.