The substance abuse center that I just began going to for individual therapy has a program for women and teens. The state funds it so, from what I understand, if you can't pay you don't have to pay. These programs may be difficult to find but they're out there.
As a person who didn't really think that AA was the right place for me, I can totally understand apprehension. After three meetings, I still don't know. What I do know is that I don't know! And until I figure it out, until I say "I gave it an honest go and it's not for me" I'm going to keep going.
I live in Chicago so there's an abundance of meetings to choose from. There are also meetings that have child care so you don't have to worry about that 3 year old. This might not be an option for you but check it out just in case.