OP you have to get out for the sake of those young children. They are also walking on eggshells, they don't have the capacity to understand why their dad is the way he is.
Living with an alcoholic is a thoroughly miserable existence and you're by yourself anyway as their primary relationship is with drink. Everything else, even their own children, come second place to drink.
Alcoholism is a progressive disease, which means it only gets worse. He's drinking around a hundred units a week, that you know of. Alcoholics tend to be secretive about their habit, for example putting vodka in drinking water bottles.
OP, you never give ultimatums you aren't prepared to follow up on because the other person knows you're not serious and won't follow through. You can't force the alcoholic to give up drinking, it simply doesn't work.
Put all that energy spent on him, on yourself and your children. Co dependent's (that's what you are) tend to expend all their energy on the alcoholic. It can feel really strange to centre yourself and not him. You need to emotionally disengage and get to the point where you're no longer concerned about him.
Useful organisations: Al Anon or CoDA
Reading: Co Dependent no More by Melodie Beattie and Co Dependency for Dummies by Darlene Lancer
Keep a gratitude journal. Get yourself a cheap notebook or pad and every day write three things in your life you are grateful for: 'Today I'm grateful for my health, for my beautiful children and for my dog'. You can also use the journal to write thoughts and feelings, (you probably feel a lot of resentment and anger) and future plans. I love lists and ticking things off lists.
Other things you can do until you're ready to leave is try something like Headspace which is Mindful Mediation. It's very powerful but it's hard, you have to keep at it, make it a habit like brushing your teeth.