(((hugs)))
Here's my thinking: It doesn't really matter whether he's drinking again or not. (See LaTeeDa's quote in my signature.) Why he's behaving in an unacceptable way doesn't really matter. When my ex does, I ask myself, "what possible explanation for his behavior is there that would make it acceptable?" -- and my answer to that question, when I'm able to be honest with myself, is always "There is none."
Sobriety and recovery, also, are not the same things. My X is sober. He's working on his recovery. Right now, he's the same angry, manipulative, hyper-sensitive, self-absorbed person he was while we were married -- he just is it sober now. Since he is involved in the care of our children, I have some reason to be aware of his recovery, as it affects the children, but to the extent it is at all possible, I've shut him and his recovery process out of my life. It's his life, his choices.
What you have to remember is that your ex's behavior in no way reflects your value, or your little girl's value. It reflects his self-obsession, his dysfunction. You have a beautiful baby girl to love and raise and enjoy. He's missing out. That's his choice. I wouldn't make that choice, but he is, and I hope you can find a way to let him go and let him make his mistakes without it affecting your balance and joy.