If it were me I would not be moving anywhere with him at this time. No trust = no relationship. Way to many lies coming out of his mouth. Pay attention to his actions, his words are meaningless.
This is great advice. What you see -- a drunk -- is what you'll get. Unfortunately all the love in the world won't stop an active alcoholic from drinking. It would be a huge mistake to make a life-changing move based on the false promises of an drunk. You and your daughter deserve so much more in life.