Can someone take kids away from their parent if the parent is a drunk?

Probably not. If the mother is truly incapacitated, the presumption is that the father would be the guardian of the children. If the father is not available, grandparents sometimes are. For a non-relative to gain custody the court would have to find that nobody else is available and can do the task properly. Her being a 'drunk' does not of itself say much about what kind of parent she is and a parent need not be perfect; none of us is. Good Luck