If you suspect and have tangible evidence of family violence, contact a family attorney to modify your ex's access to be supervised. If you have notice or knowledge of dad's propensity for violence and do not act to protect your two-year old, this could result in a CPS referral. However, prior to modification, do your homework and find out whether there is a protective order, police intervention between girlfriend and your ex, or whether there are any other convictions for family violence by dad.
It is interesting that you titled your question that you do not want your daughter to be around the girlfriend. The concern should be that your daughter is around an apparently abusive father.
I agree you should hire a local attorney to advise you on how to move forward.