Can I get a court order to prevent her new boyfriend from being around our daughter?

I recently found that my girlfriend was having secret conversations with a man. When I brought it up (she has a history of cheating), we got into a heated argument which led to her pushing me several times and striking me in face. I called the cops after she kept telling me too when I grabbed my phone. The police arrested her and she is facing assault and battery charges. We already have a custody agreement in place from a previous break up. The man she was cheating with has a history of beating up his girlfriends and I am concerned he may hurt my 9 month old daughter if she brings her around him. I told her not to talk to him at all because of this history which is well known in my small community. She doesn't seem to care about her own welfare as she is still talking with him, which kind of makes me have the attitude of, if you want to be an idiot go ahead. I don't want to take full custody of my daughter. I am a firm believer that a child needs both parents in their life. I don't have any arrest records or anything on him since I currently don't have the money for a background check. If I can't get a court order to stop him from seeing her, should I go for full custody? It is my parental responsibility to protect my daughter. I feel like it’s neglect to not do anything.