This is a difficult thing to have dawn upon you.
NO, you cannot change her, that is her job.
NO, you cannot cure her.
No, you are not at fault.
Neither are the kids.
I have a 5 year old with an alcoholic.
He lived terribly for years. I did keep our son with me, let him see the child during days, he was forbidden to drive him. HE was, though, also very aware of his alcoholism, and would not have driven him if he did get that drunk.
I made a lot of mistakes over 5 years, I tried everything you listed: threats, control.
I guess, in the end, it just comes down to your kids and their safety, and then, also, you and your sanity so you can be there for them.
Perhaps if you make the break, she will hit bottom, and take steps. But you must not take your steps to affect hers. It is a bit of a trick of the mind, finding inside of yourself the resolve to change YOUR life, and if she follows suit, then good...but you will make the change regardless.
It sounds like it has been discussed, it is no secret. She may be in denial,, and you will burst her little bubble.
But reall, since you are responsible for the kids, and since you are the only functioning, trustworthy parent, you do not really owe her an explanation for your choices. She knows. And if she cannot see it, now, she will when she is alone, and misses her kids.
What she does with that is out of your control. Some people would wake up, shape up. Others would use the "bad things that are happening to them" as a good, solid reason to drink, as if they ever need one.
Your happiness will nurture their happiness, and you making a choice for a healthy life is something they will see and learn from you.
I did my best to keep my sons father at bay when he was in bad shape. I got blamed a lot, I made bad choices, and good ones.
One of the bigger steps that I took was to put him into the child support system, and that was one in a string of wake up calls to him. He did go into treatment, eventually, and is now doing well...but it is a life long commitment.
I wish you luck and clarity in your choices.