Hey man,
My XAGF (ex alcoholic girl friend) was quite similar to your fiance. The verbal abouse was horrific. She would disappear for days, lie down in the street at night in front of our house, tell me I was gay, accused me of stealing her stuff and the best line was "I know you took my stuff, the police have it on tape?!" The first time I heard that I laughed so hard I lost my breath. She of course was absolutely serious drunk.
What I am saying to you, is this is not going to get any better. My XAGF has lost her kids, they live with their dad. I watched the whole thing unravel in court and you should take the advice and start recording and documenting now. You are not married to her and you can get the evidence, you HAVE to get the evidence.
You can no longer allow your daughter to experience this and you won't hold out much longer. It is going to effect your new job, and you may even loose it. Alcohol is a progressive disease, it is going to get worse.
Let me ask you this, if you had to get a baby sitter for your daughter would you allow someone who was an alcoholic like your fiance to watch her?