I personally think you need a plan in place before you speak to him so that you know clearly yourself what the next steps will be.
So I would talk to a solicitor and find out what you're going to need to do in terms of finances and the house, plus check the entitledto website to see what support you're entitled to financially when it comes to benefits.
That way when you speak to him you may feel calmer and more in control. And less likely to be swayed by tears and promises.
He probably wishes he could just stop drinking. He probably wishes he wasn't being a shit father and partner. But he wants alcohol more than he wants to make those wishes come true, because he is addicted.
If he is serious about changing and putting the family first then he will agree to split and work on himself to change for the better. Not threaten to harm himself and say you are overreacting and / or not 'supporting' him.
Be prepared for all those threats and have some lines you can repeat instead of getting dragged into a back and forth argument.
"I've given ultimatums before and it hasn't worked so my decision this time is final."
"The children are growing up in a home with an alcoholic and I'm not prepared to allow that to continue."
"I wish you no ill, I want you to get better and be happy so you're there for our children. I am simply putting them first as at the moment you are unable to."
"We've had this discussion numerous times and I'm not prepared to have it again, my decision to leave the relationship is final."
"I'm filing for divorce because I am putting the children first and it's not healthy for them to grow up in this environment."
Etc etc.
But I really would find out where you stand legally and financially first so that you know what your options are re next steps.