I will not accept his drunken behaviour or continuous relapses.
This is a great boundary. When are you going to start enforcing it? Because so far, you have excepted drunken behavior and continuous relapses.
Maybe you can give him the dignity and space to let him get his life in order. It doesn't sound like he's capable of a healthy relationship right now. If he's going to get better, he needs to be able to focus all his energy on his recovery. Right now he doesn't have much to offer you. Anyone can be nice when they aren't drunk. But that's not enough to base a mutually satisfying, healthy, loving relationship on.
It just doesn't sound like he'd make a great stepfather for your daughter. Ewww...
You didn't cause it. You can't control it. You can't cure it. He is who he is. And he has been that way for a really long time.
Is that good enough for you?