Stacy - I am so sorry to hear about your situation. I want you to know that I completely understand everything you described. My STBXAH drank alone as well, admitted he had an issue, resisted help, told me he could "control" it, blamed me, and was unable to be a father to our child because of his addiction.
It is incredibly hard to leave, I will not lie, for many different reasons. Guilt, fear, false hope that maybe it will get better. For me, it continued to escalate to a point of no return and the choice became obvious. My child is very young so I can only imagine that the thought of leaving is extremely hard since your children are older and aware. That said, by setting a boundary to protect them will ultimately help them. It will help them learn what is OK and what is not OK.
Be safe. Be well. Sending you good thoughts and strength to do what you need to do for your children and for you.