kin well a physically abusive (and will have been emotionally abusive too no doubt) and two partners that have cheated have clearly left her with issues. Has she had counselling? I guess you need to decide if this is enough for you, and whether you have the patience to unpick it to get you in a place you can be both be happy.
I will say, I was in a emotionally abusive relationship for 21 years, and it has affected how I proceed with dating in the future. So much so that I don't really want a serious relationship, and if people show me they are too keen, I run. I am too scared of opening myself up fully fro the wrong person. Vulnerability is scary. I do however need the physical side of things, but perhaps she finds it very difficult to seperate the two.
You sound really kind, and a good guy. If she opened up to you at the weekend, then maybe more is to come.