Hi
We have very similar situations. My mum is also an alcoholic although thankfully she is getting help. However I’ve always been wary to bring any resentments etc up with her in case she does anything like suicide as she is also depressed.
From an outside point of view I think you are doing the right thing. You have children who are your priority (congrats on the newborn!) and it is your mums responsibility to help herself, not yours. She is the parent and needs to come to the realisation that it truly isn’t acceptable to go on as she has been. If anything were to happen, it would be on her, not you.
Also, I’m being a hypocrite here as I’ve totally had the same worries as you and its a lot easier saying to someone else what you think they should do, it’s a lot harder taking the advice when it’s your own situation!!
Maybe your mum needs this to kick-start her into getting help? Maybe say to her until she gets proper help then there won’t be anymore contact? I’m not an expert so these are just suggestions ????
In the meantime, try to put her out of your head and enjoy the time with your beautiful wee kiddos. Cuddles with them heal almost anything. At the end of the day, your children are your life moving forward and I’m sure they already bring you so much joy.