Maybe wrong but it sounds to me like it's more of a problem with the intimacy part of sex that can come along with being in a relationship if it's less of a problem with hook ups??
Could it be that sort of situation makes you feel vulnerable or a lack of control in relationships? Maybe you think there's nothing to loose in hook ups, or no "judgement" coming from the guy?
A couple of things you said you "can hide it" and you "find a reason to put off sex" sound like they really can't be helping though. Do you think it's becoming something you're almost at times doing for the guy or because you feel it's expected? If so that only going to make it feel even worse for/to you.
Maybe explaining things near the beginning of a relationship might help, because it sounds like it might help if it's more on your terms/at your pace.
Now if you find someone understanding to be in a relationship with, which anyone would want anyway, maybe you could agree that you'll take the lead, at your pace. And you can have that starting off with just the contact, touching etc, etc.....it doesn't have to go all the way, not unless/until YOU feel comfortable/YOU want it to.
And you know, try to tell the guy what you like and what you don't like (or at least some hints?) so things are going more in your direction.
Maybe even try more casual touching day to day with whoever you're in a relationship with. You know arms, back etc to make touching feel more comfortable/pleasurable and not just more of a prelude to something you're not quite there on yet.
As for your parents I can see how this might have coloured your view on things, but their hang up's don't have to be your hang up's. Afterall I'm sure you don't want to follow the EXACT same paths in your life as them, we're all individual's, so maybe try to choose your path a bit more towards YOU want.
And MAYBE the way they've reacted with you was as much because you're their "child" in their eyes and they wanted to protect you from that more than that's the way they feel personally about sex. Maybe they more find it embarrassing (?) in front of you as opposed to in general. Wouldn't be uncommon with parents. Try imagining them a little differently when you aren't around perhaps, or maybe NOT??
Just some thoughts, feel free to let me know if I'm wrong and will try again.
Alison