Welcome to SR CJ. Sorry for what brings you here, it is a difficult situation for you and your family I'm sure. Ultimatums are not always effective tools, sometimes they can actually make things even worse too. I do think that setting boundaries is important though, and telling your mother that you don't want your children around while she is drinking is a fair boundary in my opinion.
At the end of the day, your mom will need to make the decision to quit on her own though. Addiction is a horribly selfish thing. and unfortunately some addicts choose their drug of choice over even family. Talking to her about it might help, but it may also backfire too. Backlash is entirely possible so you need to be preapared for it if you do approach her on the subject.