Everyone has made some excellent points. If he was serious he would already be in treatment. And if his Mother doesnt want him to be homeless she can let him stay at her house.
I would also like to point out that your daughter saw him attack you and tried to stop him. What if you let him move back and something happens to you when shes not there. Kids think everything pertains to them. I see a little girl thinking its her fault you got hurt or worse because SHE wasnt there.