I cannot relate to this post more. I have a truly messed up relationship with my mom, and I cannot imagine even talking with her on the phone sober. I don't have advice but lots of sympathy. I haven't talked to my mom in person in like two years. Can you put your sobriety first, establish a boundary, and get her out of your life for a while? It sounds like childcare is an issue here, but...you know that drinking because your mom is annoying you is irrational and silly, right?
Again, I totally relate which is why I'm trying to be straight with you. Hope you can put the booze down.
Edited to add: from what you've written, it seems really important to you that your mom understands and recognizes how hard you are working. Why? You're an adult. What is her opinion to you? My guess is that she's disappointed you by not appreciating you before. So my question to you is: assuming you can never win her approval, will you just give into drinking, then? I think you are going to need to envision the terms by which you will stay sober even when she is being a b**** (to quote you)