Yep, mother of three here. I know there are other moms on here as well. Apparently Oprah was talking about a trend in increasing alcohol abuse among moms recently -- a friend told me about the show. I'm a working mom, but I can still relate to you.
You're not a horrible mom. I don't think anyone is really prepared for motherhood -- we expect it to be a very blessed, glowing, crafty, fulfilling time in our lives and most of the time ... it's just not. Being sober will definitely help you be a better mom, though. I don't know anyone who ever said, "My mom's an alcoholic, but we always had such a great childhood!" LOL.
Make sure when you quit drinking, you work on the other stuff, too. Don't just quit and expect it all to be solved because you're sober. Quit and work on everything else, like making your life fulfilling or facing some problems you might be trying to avoid by drinking.
Welcome to SR!