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.
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.
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.
Harry might cope by retreating into his own thoughts and memories of his parents and the wizarding world. For example, he could think about the good times at Hogwarts to endure Vernon's torture.
Vernon might be jealous of Harry's magical abilities. He could see Harry as a threat to his 'normal' family life and his authority in the household.
Often, Harry's response is a mix of hurt and determination. The hurt from Snape's actions can cut deep, but it also fuels his determination to prove Snape wrong. He may strive to become better at magic, especially in areas where Snape has criticized him. He might also start to question Snape's loyalty to Dumbledore, suspecting that there's more to Snape's actions than meets the eye. This could lead him on a journey to uncover the truth about Snape in the fanfiction world.
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 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.
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.
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 this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.