If you really want your relationship to advance beyond "friends who occasionally cuddle" then you should find a way to let her know that you're open to the idea of bringing the relationship further, but you're perfectly happy letting her determine the bounds of the relationship.
Because if I know anything, it's that she's just as human as you are, and she's just as confused and conflicted as you are. Maybe even more so. Women have a lot of societal pressures to act a certain way, so you have to try to understand things from her perspective. She's had a rough childhood from the sounds of it, and some rough relationships in the past. She's afraid to take steps towards something that could make her happy because of those negative experiences. She probably has had her self confidence damaged and is afraid to take risks when it comes to relationships. It's going to be up to you to let her know that the door's open to something more happening, but she's the one who has to walk through it. That last bit's very important. Neither of you should hop into something that you're unwilling to do.
How exactly you let her know about this is up to you, and you can be as subtle or as blunt as you want.
My advice? Be frank. Tell her up straight in the gentlest way possible. Reading the tea leaves can be the worst part of trying to progress a relationship, and it's difficult enough when you're dealing with someone who's confident and is willing to take risks. Your friend isn't either of those, and while it should be a goal of yours to encourage her to be more confident and happier, that doesn't mean that you can't try out for a steady relationship until then. Heck, part of her lack of self confidence could be because she doesn't know why you don't try to progress the relationship. Men are expected to be the instigators after all.
Find a good time, when you're alone and it's quiet. Ask her if you can ask a question, then ask her if she's willing to let your relationship progress beyond what it is now. Leave what your relationship actually is to be ambiguous, since she may see it differently than you. The important thing here is to let her know that you're open to the idea (But don't be desperate, and if you are, don't let her see that), and that you're willing to let her be the one who determines how fast things go.
At this point she may be worried that you're just after sex, so be careful about making any innuendo: Sex can be part of a relationship, but it's not what makes relationship. Judging from her reactions to being with you she may have had some bad experiences that started with just a little physical contact, so it's best to let her determine when something like that will progress (So long as you're comfortable with it, naturally - It's a two way street, and you should meet in the middle).
So just tell her. The friend zone sucks, but the most likely culprit is that she doesn't know that you're willing to get out of the friend zone and have a serious relationship. She may also have some trust issues that have nothing to do with you, so don't push into territory you're not sure she's willing to go.
As for everything else having to do with her mother... I can't give much advice there, other than that it'll probably be an issue until she gains some self-confidence and self-worth, and even then it could be an issue for her. Just focus on the two of you for now, since that's all that's really important, and be there to help her out if she needs it.
Good luck. I hope everything works out.