This might sound like the stereotypical answer and not be much help, but it might be good to have a face-to-face conversation with them and tell them everything--about how you feel, what you think, what you want, the effects their abuse had on you. I guess it's technically called "closure" or whatever, but no matter the technical term, maybe talking to them face-to-face about it at least once would help you.

Also, if you're doing well with them outside of your life then you might just need to stay away from them for a while before communicating again. Sometimes choosing distance is the best way to deal with a problem before trying to rebuild the relationship--even with parents.

I don't have personal experience in the kind of situation you're in, but I hope this helped.