Like everyone else I see huge red flags in this, most of all that your own instinct is causing you to question the wisdom of this relationship.
A lifetime alcoholic, multiple marriages and rehabs, a dry drunk who speaks with pride of his alcoholic past - all huge red flags.
I totally understand that you want this to work out and there are some good qualities to this guy. That he wants to go slow is one of them. Go very, very slow and LISTEN to your instincts, which seem to be saying to forget him. He doesn't talk with pride about his past in front of your daughter YET. What would you do if he did?
Good luck to you.