You didn't cause it. You can't control it. You can't cure it.
Even if your behaviour is part of the problem, doesn't that just make it even clearer that you aren't helping him? (in the long term with the stuff that really matters - obviously you 'help' him with the day to day things to keep him functioning) And that leaving will give him the opportunity to either carry on much as he is but with takeaways instead of home cooked meals, or to get genuine real help to get better. And either way you and the girls will be better off?
Forget about blame at the situation. No one here is in the "You made your bed, you lie in it" mentality. You are in a crap situation that's making you ill. Disregarding whose fault it is, what can you do to improve it? Because he's not capable of improving things for you and the girls at the moment or in the foreseeable future.
And you are likely to get more long lasting success by taking that step to ending the relationship, because tinkering at the edges of exactly how many drinks he has at each night, or whether he makes a clumsy attempt at trying to be a good dad, isn't going to be enough to make you all happy. Look after yourself and your DDs and give him the opportunity to stand up and look after himself.
Its not the sort of illness that you can stand by and support him through. His misery cannot forever make your happiness and freedom take a back seat. Its good that you want your children to learn kindness, but that isn't what this is. Enduring sexual contact you do not want is not a kindness to him, its an betrayl of you. There is being a loving generous person who gives what they can afford to, and there is standing still while someone robs you of the last of the most basic nourishment to keep you going. You will both end up crashing.
On flights during the safety demonstation, if the air supply is compromised, oxygen masks are released from the sealing. Passengers are advised to fit their own masks first before they help their neighbours, even if those are their children. The reason is that if you pass out from lack of oxygen, you are no use to anybody. Its not heroic to not look after yourself.
Its time to put on your oxygen mask. Save yourself, it will give you the strength to help others. Then save your daughters. Then, once you have secured your mental and physical safety, from a distance, you can point him in the direction of real support - AA, his GP, etc and he can find others I'm sure.
I think you need to let go of your huge sense of responsibility past, present and future for his behaviour. He has been vile and abusive towards you, at the very least he has not been a full and equal partner. He is not some child or pet that you are beholden to, he is an adult, and if he isn't capable of standing on his own two feet, he needs professional help. You did your best but it will never be enough for him.
You didn't cause it, you can't contol it, you can't cure it.