My ex said exactly the same stuff, there was no way I was moving out since only my name was on the mortgage and with his drinking there was no way I was going to agree to split custody. In the end he moved out, we split everything 50/50 and I got physical custody of our son.
I had years and years of evidence of his drinking, I told him "if you fight me you'd better be ready to bring it because I will roast your a** over an open fire in court".