I think that, despite John’s trainings and insistences that the girls learn how to hunt, he would most likely try to enforce some outdated gender views - they shouldn’t ask too much, should at least know how to cook and clean, should be pretty and have long hair. Sam, being the obedient daughter that she was, would definitely rebel and lop off a good chunk of her hair with one of their hunting knives after a nasty argument (and she would be horrified at the end result. Deanna would try her very best to tame it down and make it look as presentable as possible with their limited array of knives, because even then, even when Sammy was being difficult, arguing with Dad again, she hated seeing her little sister cry).
There is absolutely no doubt that Sam was set on the idea of normalcy - white picket fence, a house, school. She tried to be low-key, to blend in with all the other nondescript masses she admired and envied. But even when she felt she was as close to normal as she could ever get, she still felt different - the odd piece of a puzzle that fitted nowhere. A freak. And that only amplified when she hit her growth spurt and started looking significantly different from her curvy sister; she was too tall, her shoulders too broad, her hips too narrow, and what she wouldn’t give to be… normal.
And even when they’re older and her hair is longer and she’s grown into her frame, she still feels like the odd one out in their trio. Deanna is The Righteous, Castiel is an Angel of the Lord, Sam is Azazel’s Queen. Even after the Apocalypse, after she cast herself into hell and was pulled out, she still feels that there’s still something not quite right in her. She’s still that puzzle piece who can’t quite fit in.