This is such a tough question. I am going through something similar myself.
I'd personally like to believe that people are capable of change. That a few poor choices and actions of abuse do not "make the person" so to speak.. obviously there's a lot more about this man because at one point you liked him enough to have children with him
I find it hard to keep that in mind with my ex sometimes but I know it must be true.
I think not having a father is better than having a father who emotionally or physically abuses you. Conversely I do think that if the father is wanting to genuinely be a better parent he should be given that option, certainly..
I left my daughters father when he threw her on our bed as a newborn.. I found it very difficuly to let him have her for weekend visits, and worried what was going on. At the same time I wanted very much for them to have each other, (he is a good playmate and they have fun together when hes around)..
Sometimes I'm scared that I made a bad choice, that I was not being a good mother in letting him be alone with her, but I have no real reason to believe he hurt her ever again, and had no right to tell him no anyway.
Its a tough choice, and in a lot of cases one you dont have any say anyway (if the courts grant him access for example).
Good luck