Welcome, tinker,
I've been where you are (shorter time period, no kids involved, thank God), and I agree, it makes no sense. Alcoholism makes no sense.
Glad you are in Al-Anon--it was my lifeline when I was making the stay/go decision. Nobody can help you decide what your own limits are--when to go, for example--but it will help you keep sane through the process of making decisions that are in your and the kids' best interests.
As Pelican said, there is always hope that the alcoholic may recover. Sometimes it doesn't happen until years after they've lost their families.
Keep breathing. Stick around here--there is great support available 24/7.