1. He lied to you about keeping in contact with girls he was with last summer.
2. He drinks in sufficient quantity to get drunk.
3. He is an abusive drunk.
4. He has cheated on you.
I don't understand why you're even living with him in the first place, much less be confused as to what to say to a marriage proposal under these circumstances.
Pack your and your daughter's things, get the heck out of there and don't think twice about it even if he makes contact afterward and tries to apologize.
A guy like that changes his behavior about as often as a leopard changes its spots for stripes.
