Hi ~ I wish I knew what to tell you. Since you didn't say if you were in AA or not, you should know that being honest is one of the most important things in recovering from alcoholism. Once you tell a lie, you have to keep telliing lies to cover up the first one. It's a vicious circle. And it always ends badly.
If you ever want anyone to trust you, you must be HONEST.
Also, do you think it's in the best interests of your CHILD to leave her in the car of your wife who is a "raging alcoholic?" It would seem to me that the child is in DANGER. If you're not home, you should make other arrangements for the child, and NOT leave her in the care of her mother!!!
As for your girlfriend -- she may have heard that you still have a wife, and wants to think things over. Perhaps she doesn't trust you now.

I know that if I were her, it would effect me badly, and I would wonder about the relationship.

I certainly would not want to be running around with a married man!
You'll find out soon what the problem is. But you are going to have to be honest with her. Whatever the outcome is, I wish you luck. God bless and please take care! Hugs, Lee

PS -- if the outcome is bad, DON'T DRINK!!!