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Petunia Evans is muggleborn just like Lily. She attends Hogwarts two years earlier than her sister and ends up in Slytherin.
Petunia likes to think of herself as special. She has magic in a family of muggles and she's a muggleborn in Slytherin. Still, the other Slytherins don't take to her quite as well, and Petunia finds herself on the receiving end of their ire often, but Horace Slughorn, who's the head of Slytherin house, usually puts a stop to it.
And then it turns out that Lily is also magical, and Petunia's a bit miffed about it. Hmph, her little sister just stole the thing that made her special, and now she has to share.
Still, Lily is so happy that she's got magic too that Petunia doesn't quite have the heart in her to hate her adorable little sister forever.
Her jealousy festers a bit more in Hogwarts when Slughorn invites Lily to the Slug Club instead of her. Seriously, Petunia is in Slytherin and she's older, but Lily got it right off the bat. And for what, being good at potions?
Petunia manages to convince Severus to help her with her studies so she could prove herself to be just as good as, if not better than, Lily. Spite is a powerful motivator. Severus doesn't really like Petunia that much because she's whiny at times, but eventually he gives in.
The Marauders help a little too, since they're all friends with the Evans and Severus in this AU. Basically Petunia, with her nose for gossip and scandal, quickly clocked in on the fact that James has a crush on her sister. Being a sneaky Slytherin, she gave him an offer to help set him up with Lily, and in return she gets a couple of favors. The Marauders are prodigies, after all, and James' invisibility cloak and the Marauders' Map are invaluable.
Petunia's advice involves deflating James' head and being nice to Severus. Apologies work wonders, and groveling helps. So the Marauders don't bully Severus, and Lily thinks better of James.
Lily, Severus, and Petunia end up sort of joining them. Petunia very quickly figures out that Remus is a werewolf around the same time his closer friends do. To be honest, she's mildly tempted to blackmail him on it, but she's nice enough not to.
So instead, Petunia, Lily, and Severus turn into animagi with the Marauders.
Their Marauder forms and names are flying fox and Hooky for Severus, fox and Foxtrot for Petunia, and lioness and Ginger for Lily. Her fur's still a bit fiery red in animagus form, you see. The rules for Marauder names is that you can't pick your own name, someone has to do it for you and you can only veto it if there's a very good reason, and they have to take the mickey out of you in some endearing way.
Also, the defense professors are just as bad as the ones in canon because this curse has been going on for a while and is still coming up with new ideas.