Sweetie, I dont want to be horrible, but you are being blinded by how your DD feels about him, and taking that over what kind of man you know he really is. The man who beat you to a pulp.
Do you honestly think that a man who will batter his OH, who hates her so much that he controls her every move, will just let her go?
No, he will use any means he can to continue to control you and moreover, to PUNISH you. He knows he cant hit you anymore as you wont take it. So what else will he have if he isnt living with you? Your DD.
Believe me, there are people out there that will do ANYTHING to a child if they think it will hurt their ex.
HE IS NOT NORMAL, HE IS NOT KIND, HE IS A VERY VERY BAD FATHER AND YOU ARE WRONG TO THINK OTHERWISE.
Sorry, but there it is.
Calling social services and alleging abuse, getting others onside to get custody, saying cruel and vicious things that fuck a child up for life..... none of these are unusual. He should be kept away from you for life, and kept at arms length from your DD. He ISNT safe to be around her! And the only way you will get supervised access is to get him convicted of domestic abuse.
Forget what it will do to him, google what some parents do to their children in the name of getting back at an ex, and PROTECT HER.