Man! This whole thing reads like disaster x 10. It's a lot. Changes have to be made, certainly. I can't really comment about her because I don't know her view of things and there's no way to sort that out. I can only comment on what you have said. With the trauma and all, she's going to need help. Forever. It's a horrible thing, rape. Are you ready to deal with that and everything that goes along with it? It's a lot of responsibility. If you're not ready, than you owe her the chance to work that out.
You have to decide, and when I say decide, I mean just that. Not because she's hot, or young, or the great drunken sex, and all of that. That means nothing. A relationship can often survive with a good friendship and mediocre sex. But a relationship can never survive with a mediocre friendship and great sex.
So, I would suggest making a carefully thought out decision and stick to it. Don't buckle. Lot of great replies here. If you move just to get away from things, you tend to just take your problems with you. If you leave because you've carefully weighed all your options and decided to do it with a clear head, then the outcome is more positive.
But no matter what scenario you choose, make sure it's your decision. Stick by your own decision firmly because of it's logic. Not a rash decision all tied up in knots with emotions and horniness and all that other BS because in the end, it will just be you and her. Do you love her? Is all the work what you want? Or maybe not. Maybe you want something else for your life.
There is a lot written here but it really all comes down to that in it's simplicity. You take out the sex, the drinking, the trauma, the hotness, the dysfunction, and what are you really left with? And is whatever that is worth it? Then put in the work and make it happen. On the other hand, if what you're left with isn't worth it? Then move along, or move away, or just make a decision and do that. But stay in control and run your life. Because it sounds like your life is running you. The tail is wagging the dog. That's not a good place to be.