You can't really "ensure your daughter doesn't drink again." It isn't just a matter of being "nosy," but trying to control someone else's drinking is exhausting and futile. I'm glad you're there for the baby, but these are some tricky waters you're trying to navigate.
Have you been to Al-Anon? With the previous marriage and now your daughter's issues, living with alcoholism has probably affected you pretty deeply. If you haven't been, now might be a very good time to start.