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.
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.
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.
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.
I'm not sure if there are 'popular' ones in the sense that they are widely known and accepted. Lemon fanfictions are a bit of a niche and often not mainstream due to their mature content. But there might be some that have a following within the more hardcore Harry Potter fanfiction community.
One interesting 'Harry Potter Petunia Dursley' fanfic could be one that explores Petunia's childhood and how her relationship with Lily might have affected her view of Harry. For example, a fanfic could show that deep down, Petunia was always a bit envious of Lily's magical abilities, but also loved her sister in a complicated way. This envy could have then translated into her cold treatment of Harry.
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 fanfiction could be about Petunia Dursley having a secret love for lemon - flavored treats and how it changes her mood. For example, she discovers a new lemon cake recipe and it makes her momentarily forget her usual grumpiness.
Some fanfictions might involve Petunia Dursley's relationship with lemons in a more comical way. Maybe she tries to make a lemon - based household cleaner that ends up having some very unexpected and humorous results, like turning the whole kitchen a bright yellow color or making a strange smell that attracts magical creatures.
Maybe she secretly has a soft spot for the magical world she once shunned. Fanfiction might offer her a different perspective on Harry's life, one that she can explore without fully admitting her growing curiosity or even a latent affection for the boy she once treated so poorly.