It is not good for you, your girlfriend, or your child to try to force an abusive relationship to work. Do you want your child to grow up thinking it is okay to beat around a spouse? Do you want her to be fearful that if she angers someone, she will get yelled at or hit? I know it would be very tough to let your daughter go, but the relationship will not be good for her development.
Is she ever this way toward your daughter? If she is proven abusive, will that affect custody?
It sounds to me like she thinks she can treat you however she wants and just hold your child over your head. It does not sound to me like she wants to be in the relationship, but will use your support. I would say to talk to her about couples counseling, but how do you think she would react to that?