Call me crazy, but I was pretty surprised when I found out Aunt Petunia had written to Dumbledore, begging to be admitted to Hogwarts. In Philosopher's Stone, Petunia shrieks about Lily, admitting that she knew all along that Lily and James - and Harry, by default - were magical.
"How could you not be, my dratted sister being what she was? Oh, she got a letter just like that and disappeared off to that - that school - and came home every holiday with her pockets full of frog-spawn, turning teacups into rats. I was the only one who saw her for what she was - a freak!... of course I knew you'd be just the same, just as strange, just as - as - abnormal - and then, if you please, she went and got herself blown up and we got landed with you!"Knowing Petunia's attitude towards the wizarding world, I didn't expect that she'd wanted much to do with it. I didn't even consider that she would have been close to Lily. She was "proud to say that [she] was perfectly normal, thank you very much".
However, in Deathly Hallows, all was revealed.
Petunia wanted to be a 'freak' as well.
She caught her sister's hand and held tight to it, even though Petunia tried to pull it away. "Maybe once I'm there - no, listen, Tuney! Maybe once I'm there, I'll be able to go to Professor Dumbledore and persuade him to change his mind!""I don't - want - to - go!" said Petunia, and she dragged her hand back out of her sister's grasp. "You think I want to go to some stupid castle and learn to be a - a -"Her pale eyes roved over the platform, over the cats mewling in their owners' arms, over the owls fluttering and hooting at each other in cages, over the students, some already in their long, black robes, loading trunks onto the scarlet steam engine or else greeting one another with glad cries after a summer apart." - you think I want to be a - a freak?"Lily's eyes filled with tears as Petunia succeeded in tugging her hand away."I'm not a freak," said Lily. "That's a horrible thing to say.""That's where you're going," said Petunia with relish. "A special school for freaks. You and that Snape boy... weirdos, that's what you two are. It's good you're being separated from normal people. It's for our safety."Lily glanced back towards her parents, who were looking around the platform with an air of wholehearted enjoyment, drinking in the scene. Then she looked back at her sister, and her voice was low and fierce."You didn't think it was such a freak's school when you wrote to the Headmaster and begged him to take you."But, obviously, Petunia wasn't accepted.
I don't know why, but I often wonder that had Petunia held the mild interest in it that her parents held, rather than the desire to do what Lily did, and the jealousy that stemmed from being left behind - would Harry have grown up differently?
Who knows. Silly question, anyway, when the books are fabulous as they are.
Note: Quite obviously, all that text above is copyright of JK Rowling.