He is an ACTIVE alcoholic, not in detox, and benzos mixed with alcohol are a deadly combination.
Unless this is a medically-supervised detox, I think the doctor is inappropriately giving an addictive narcotic to an active addict.
I would continue to view your AH as someone in active addiction (back pain and vomiting, by the way, could be related to opiate abuse which is very hard to detect). And I would prepare for more chaos.
Do what is best for your children and you.