In addition to Harry and the Dursleys, there could be some Hogwarts professors involved. For example, Professor Dumbledore might play a role. He could be the one who arranges for some sort of exchange or interaction between Hogwarts and the Dursleys. Also, Hermione and Ron could be main characters if they accompany Harry to meet the Dursleys or are involved in the events that bring Hogwarts to the Dursleys' doorstep.
Perhaps in the fanfiction, Hogwarts decides to send a group of students to study the Muggle world up close with the Dursleys as their hosts. But what if the Dursleys are secretly working for a dark wizard who wants to use this opportunity to infiltrate Hogwarts? That would be a huge plot twist.
Well, Daphne in the 'Daphne meets the Dursleys fanfiction' would probably interact with the Dursleys in a very cautious way at the start. She would be observing their behavior towards Harry closely. Once she realizes the extent of their nastiness, she could try different approaches. She might try to reason with them, explaining how wrong it is to treat a child like that. When that doesn't work, she could use her magical abilities to disrupt their daily routine in a harmless but annoying way, like making the TV constantly change channels or the kettle never boil. This would be her way of getting back at them for their treatment of Harry and also a way to show them that there are forces they don't understand.
Snape would likely be disdainful towards the Dursleys. He has little patience for Muggles in general, and the Dursleys' mean - spiritedness would not endear them to him. He might use his cold, sarcastic tone on them, leaving them confused and a bit frightened.
Perhaps Snape would initially mistake the Dursleys for some sort of Muggles with a bit of dark magic in them due to their cruel nature. He could start investigating them, which would cause chaos in the Dursley household as they try to hide their secrets from a wizard like Snape.
In the 'Daphne meets the Dursleys fanfiction', it's possible that Daphne initially has a hard time understanding the Muggle - like ways of the Dursleys. However, as time passes, she might start to see through their facade. She could then form a plan to get Harry out of that unpleasant environment. For example, she could pretend to be a social worker or something similar in the Muggle world and convince the Dursleys to let Harry go with her. And then she could introduce Harry to the wizarding world in a more positive and gentle way than how the Dursleys have been treating him.
One possibility is that Remus meets the Dursleys when he is on some sort of mission related to Harry. He could be there to assess the safety of Harry's living situation. He might find the Dursleys' treatment of Harry unacceptable and try to subtly change things. He could offer to help around the house in a very civilized way, making the Dursleys a bit confused as they are not used to such kindness from the wizarding world. This could lead to a series of events where the Dursleys start to question their own views about wizards and witches.