You say she has family problems (dysfunctional family). A dysfunctional family is actually a very serious thing and it's effects are extensive. It teaches a GOOD and loving person poor self-esteem. It teaches them to belittle, ridicule and criticize themself and mock and mistreat whatever would bring them happiness because of their inability to feel deserving of happiness (she will push away what she doesn't feel deserving of). Their reference point of understanding this world is that they are guests on this world of those who can find a use for them. She reacts to you with fear because she doesn't know how to deal with genuine, true blue emotion. Properly handled, her family will be getting jealous of you. You can explain this to her and she will, at first, say this is not true, but she will eventually understand that she is doing this. If she explains this to her family, they will be dead set against you (feel defensive), so I don't advise that this understanding goes beyond your relationship.