One reason could be jealousy. Maybe she's jealous of the magical world that her sister Lily was a part of. She might feel left out or inferior, which could lead to her anger.
I'm not sure of specific 'angry petunia dursley fanfic' off the top of my head. But you can try searching on fanfiction - specific websites like Archive of Our Own. They have a large collection of fan - fictions and you might be able to find some related to an angry Petunia Dursley there.
One possible fanfic could be about Petunia Dursley finding a magical toy that once belonged to Harry Potter's parents. Maybe she discovers it in the attic and it starts to show her memories of Lily and James Potter. She realizes that she has been wrong about Harry all along and decides to change her attitude towards him.
By focusing on their shared past traumas. For example, both have had experiences related to Lily's death in different ways. Harry lost his mother, and Petunia lost her sister. They could start to bond over this common pain and gradually move towards a more positive relationship.
In a more comical plot, the lemon could be a mischievous magical object that keeps causing chaos in Petunia's house. It might make things float or turn into strange creatures. Petunia, being the uptight person she is, has to deal with this lemon - induced mayhem while also trying to keep up appearances in front of the neighbors. This could lead to some really funny situations and a change in her attitude towards the strange and magical over time.
A fanfic could connect them by having a toy that was passed down from Lily Potter to Harry, but Petunia has kept it hidden all these years. When Harry discovers it, it causes a big conflict as Petunia doesn't want to let go of the last piece of her sister she has in that way. But eventually, it could lead to a moment of reconciliation between them.
One good aspect is the exploration of their family ties. Petunia is Harry's aunt, and despite her coldness, there could be a deeper connection beneath the surface. Another aspect is how Petunia's Muggle perspective clashes with Harry's magical world.
Petunia Dursley is significant as she represents the non - magical world's reaction to magic in the Harry Potter series. She is a Muggle who has a complex relationship with the magical world. She has seen magic through her sister but resents it. Her actions towards Harry, like treating him as an outcast in her home, show how some Muggles might fear or be envious of the magical abilities they don't possess.
There are indeed appropriate fanfics. Some may center around Petunia Dursley's early life and how it influenced her treatment of Harry. It could be about her jealousy of Lily's magic and how she eventually comes to terms with Harry's presence in her life in a way that is more about family drama and less about anything inappropriate.
One way could be to explore her relationship with Lily before the events of the main series. You could write about their childhood, how their differences started to emerge, and how Petunia felt about Lily's magical abilities at that time.