Speaking from the alcoholic point of view. It was only when I realized that my alcoholism was just a slow suicide that was not only killing me but everyone around me that I finally knew that I had to find a way to live without the alcohol or find a way to hurry up and die. This realization did not come because of the thought of losing anyone or anything in particular. It was just the culmination of my life as an active alcoholic. I had to get to the point where I surrendered to the fact that I could not control my alcoholism and that it was destroying my life. My thoughts are that I was beyond human aid. It did not matter how much I cared about my children or anyone else, even the thought of losing them could not have stopped me from drinking. I am fortunate that I was led to A.A. and I was desperate enough to go to any lengths.
I can not speak from an ALANON point of view as my experience in that area is quite limited. I did start going to meetings a few months a go but not on a regular basis. I do think that we need to take care of ourselves, not necessarily at the expense of others but we have to realize that others make their own choices and are responsible for them. It sounds like you are ultimately asking when would it be appropriate to leave? Will an ultimatum work to get him to stop drinking? and Is there any hope for him? My thoughts are you need to make yourself and your children your priority. Although he is a sick man, he is still an adult who is responsible for his own choices. I would not base my decision to leave or not to leave on whether or not he will get better. I would base the decision on what is right for my children and myself. I can not say that there is no hope for him to get better but ultimately that comes down to if and when he is ready to do whatever it takes to live sober. As far as an ultimatum, I do not see where it would make much of a difference either way, he is either going to quit or he is not. Many who quit drinking to save their marraige or for reasons outside themselves are unable to maintain any length of sobriety.
You make the statement that when you leave, you leave for good. To me that sounds like you probably have your mind made up as to what you need to do. I would suggest though that if you choose to leave consider leaving that door open (but don't necessarily let him know that). The reason I say that is there is a part of hiim that you loved enough to marry and have children with and hopefully if he is able to get sober that person will come out again.
These are only my thoughts on the subject, not advice, or telling you what to do. Take care, I pray that whatever choices you make you and your family find peace.