I agree with everyone else. Do get therapy, and see a pdoc. You know showing her that kind of anger could keep her away from you. Not to be mean, but I would have left also.
It's not cool at all that her parents don't want you around her. From what your saying it's the jail thing. I'm not sure, but I think that it is more then that. The reason why I'm saying this, is that I have a 17 year old, (almost 18) she was dating a guy who I did not approve of. The reason? I didn't like how he was treating her. If he would have made an honest effort to change somethings in his life, then I would have been more accepting to him. It is also something for you to think about your gf having to sneak to be around you. If you want her to come around more without sneaking, then it is up to you to make things right with her parents. I'm not trying to be harsh, but if my daughter told me that she was dating a guy who gets mad at her, and breaks things when he is angry, then I am going to tell her that I don't want her to be around him. If her parents know this about you then I think that they are worried about her safety.
One thing that I would like to say is the past is the past. What your gf did in her past, should be left in her past. She can't change it. You could really be making her feel very uncomfortable by bringing it up all the time. We all have have things in our past that we arent proud of, and it's like your smacking her in the face with it. If you can't take her for the person that she is, then maybe it's time to say goodbye to the relationship. I will say this. It would be really smart of you to clear up the mess with her parents. If you really want her in your life then take care of that. It's just not fair to your gf at all.