In such a fanfiction, Hermione's encounter with the Dursleys could be full of drama. Since Hermione is a clever witch, she may use her magic knowledge to expose the Dursleys' ill - treatment of Harry. For example, she could magically make Dudley see how wrong his parents' actions are. At the same time, she may also try to bridge the gap between the wizarding world and the Dursleys, though it would be a difficult task considering the Dursleys' deep - rooted dislike for anything magical. However, Hermione's determination might bring some unexpected changes to the Dursleys' household.
One possible plot twist could be that the Dursleys are actually under a spell that makes them act so horribly, and Hermione discovers and breaks it. Another could be that Hermione finds out she has some family connection to the Dursleys, which would be a huge shock for everyone.
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.
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.