It might show their fear in a more extreme way. Instead of just being dismissive of magic, they could be absolutely terrified of it. For example, every time Harry does something even slightly magical, they could cower in a corner.
In this fanfic, the Dursleys may be depicted as being in over their heads. Vernon Dursley, for example, might be shown as constantly angry and trying to assert his authority in a situation where he has none. Petunia Dursley could be portrayed as being torn between her dislike for magic and her sense of family obligation towards Harry. Dudley might be shown as being bullied or affected in the Muggle world because of Harry's presence in their family.
One possible plotline could be how the Dursleys face magical mishaps in their daily lives that drive them crazy. For example, maybe Dudley accidentally gets turned into a pig by a stray spell and the Dursleys have to deal with that chaos. Another could be that they are constantly haunted by strange magical creatures that are attracted to Harry's presence in their house.
Well, perhaps the arrival of Harry Potter in their lives could be a major factor. His presence might disrupt their normal, mundane existence. They are forced to take care of a wizard child while they are Muggles who seem to despise anything out of the ordinary. His magical outbursts and the constant reminders of the wizarding world that come with him could be making their lives a living hell.
A lot of fanfictions play around with the Dursleys' relationship with Harry. They could be depicted as having a sort of begrudging respect for Harry. For instance, when Harry starts to show real courage and power, the Dursleys might start to see him in a new light. This is different from the original story where they mostly just try to suppress Harry. Also, some fanfictions might give the Dursleys magical abilities of their own, which completely changes their dynamic with Harry and the wizarding world.
It might show the constant power struggle between them. Harry, as a wizard, has an inner strength that the Dursleys try to suppress with their mundane and cruel ways. So it's a battle of wills.
Well, Sirius Black could be an interesting character to put in a 'Harry Potter Dursleys fanfic'. Since he was Harry's godfather, his presence could stir things up for the Dursleys. He might be furious at how they treated Harry and take some sort of action. Hermione and Ron could also be included. They could visit Harry at the Dursleys' and be shocked at the living conditions. Their reactions and how they interact with the Dursleys could make for an exciting plot. And of course, the Weasley family as a whole. Their warm and loving nature would contrast greatly with the cold Dursleys.
Definitely Dudley. In fanfic, he can be developed in so many different ways. He could become a wizard himself, or he could befriend Harry in a more meaningful way than in the original books. Another interesting character is Petunia. There could be more exploration of her past and her relationship with Lily, which can make her character more complex.
In many of these fanfics, there could be a new character introduced, like an old wizard who lives in the neighborhood secretly and notices Harry's situation. This character might play a crucial role in helping Harry deal with the Dursleys and his growing magical powers. He could be a mentor figure for Harry, guiding him through the tough times.
Mrs. Dursley was Mrs. Potter's sister, but the Dursleys treated Harry Potter badly. They never treated him as their own son, almost abusing him. They hid Harry's magical identity, which made Harry confused about his birth and the magical world in the first book. This kind of bad behavior was mainly psychological damage. Harry Potter and the Sorcerer's Stone was not enough. Everyone, please click to read the novel!
Dumbledore might play a role. He could be the one who encourages Harry to stand up to the Dursleys. He might have some hidden knowledge about the relationship between the wizarding world and the Dursleys that could help Harry. Also, Hagrid could be involved. He could provide some muscle if things get physical. He might also offer some emotional support to Harry, as he's always been like a big, friendly giant to him.