P.S. One of the most helpful things I ever learned in my life was when I was doing the "Ambulance thing" from a Paramedic I used to work with called:
Subjective
Objective
Analysis
Plan
SOAP
I was NEVER allowed to make a diagnosis, what I had to "report" was "what I heard", what I saw with my own eyes, what my analysis was, and what my plan was.
Subjective is what was told to me, or in this case, what my head was telling me
Objective is EXACTLY what I view with my own eyes
Analysis is what I think by assessing both the subjective and objective data
Plan is "what am I going to do to resolve this situation
So what would "SOAP" be in your situation?
rather then "diagnosing" him as suffering from untreated alcoholism, taking all your "feeling statements" and put them together
Then all of your "objective" data, such as his refusal to attend therapy on his own, you and your childrens comfort level when he is there, when he is gone etc.
Analysis of what YOU can do FOR YOURSELF to resolve this, whether it be acceptance or change (yourself and your acceptance level) or leaving him.
Make and execute your plan.
If you can observe and describe what is really going on without placing any emotional value on his behavior, I mean by making him "wrong" or "bad", just this behavior makes me feel ______, I find that I make much better decisions from that place.
Anyway, this is an exercise that has yielded amazing results for me in the past and has allowed to make much more intelligent decisions that were actually based on reality.
He may be an untreated alcoholic, he may have just been a heavy drinker, the questions are about YOU, and what YOU want in your life and what makes YOU happy.
I remember talking to my therapist and crying out, "I don't know what to do, tell me what to do" and she always said "yes you do Andrew, you know exactly what to do, you just aren't ready to do it yet"
I said, "How do you know I know what to do?? I'm so confused!!!"
She said "Because you told me"
You have the information, you have given us the information, go back and reread all your posts, and your answers are written in every post.
Working on yourself lets you learn to be clear about your decisions, and why you are making them.
Take it slow, take it easy, keep on doing what you are doing, and it will work out exactly the way it supposed to.