Sasha, If it looks like a duck and walks like a duck, it is a duck. Chances are your AH is not only lying to you about his drinking, but to his AA group.
"I heard that he got his one year chip last month so I don't think he is drinking again." He's, also, lying to himself!
WHO ME? I'M NOT DRINKING!****** 
Here on SR we call the lies that alcoholics tell us as
"quacking"!
Please stop blaming yourself about getting involved with this alcoholic! It would be nice if all the alcoholics would walk around with a BIG red
"A" stamped on their foreheads, but unfortunately, they don't. Alcoholics are like chameleons; they can change their personalities to suit their environments.
You wrote
"I constantly pray that I can let this go. And accept that he has denied his little girl, but the pain continues to be intense. As does the rage." Hopefully, after you call the California Department of Child Support Services
California Department of Child Support Services > Home some of your anger and pain will diminish!
Attend as many Al-Anon meetings as you, start with the counseling service, and keep posting here on SR. We're here for you! :ghug3 Give your little one a hug from me!
Just my personal opinion. Take what you like and leave the rest.
Love and Peace,
Phoenix