Saying that you don't want your mother around your baby when she has been drinking - or even quietly committing yourself to the fact that you will not allow the baby to be with her alone and unsupervised (in case she has been drinking and you are not aware) are both fair enough and in fact very, very sensible.
Saying she cannot see your child full stop (even when she is temporarily sober) is not fair enough in my opinion - and a little bit hamfisted if not cruel. I'm sorry that you won't like that push back.
Furthermore - ultimatums like this don't work anyway as a long term recovery program.
I suspect I'll get some flak for not towing the line on this, but that's my honest take on it. Find some middle ground.
Regards,
JT