You are desperately unhappy. Alone, you are shouldering the burden of being the responsible adult in the house looking after not just the home and children but also a dysfunctional adult.
I read a lot of threads on here by people who are desperately unhappy, but because they have coped with so much, have learned to live with such ill treatment, they are convinced that "its not bad enough to leave", they cite how much worse it could be "he's not a violent drunk" or "he's not very physical, it was just a shove" etc.
In truth there is only one thing you need to know before making the decision to end a relationship. It is that you do not want to be in the relationship any more . You don't have to pass some test of how awful the other person is or justify your reasons to him or anyone else. You've had enough.
As it happens, there is a heck of a lot of people who would think that drinking every night, getting stoned every night, being emotionally absent, leaving the other partner to do almost all the chores and childcare, being sexually pushy (and yes, abusive, you should never be in a position of being scared to say no, even if that fear doesn't come from what the person will do to you but to themselves) are all pretty darn good reasons to run for the hills.
The problem is, you are coping and surviving these circumstances, which is good in the short term, because surviving is good obviously. But it makes you think that "it's not too bad, I've coped up till now, I can handle it" and makes you stay, much longer than is healthy for you.
Please believe us that we have heard that you don't consider him the worst kind of drunk. It doesn't matter, it's bad enough that he is controlling and damaging your life (and that of your children though you may not realise it till they are no longer living with him).
You also seem to think that you are not a typical spouse of an alcoholic. I don't know what is typical, and maybe it is true that what you've looked at of these support groups doesn't ring true to you. But, you have said things, about not wanting to hurt him, needing to protect him, being responsible for him that make me think that some form of support for you (be it one to one counselling, or a group support or both) while you are leaving him would be a good idea. You might not feel that you are co-dependant, that you don't enjoy being needed by him - and maybe you aren't. But you are in a situation where you feel responsible for protecting his feelings to the extent that you end up freezing and being subjected to sexual contact that you do not wish to have. Where you are so busy trying to keep everything normal (making sure he is fed, that the children and home are looked after) that he isn't able to feel the consequences of his actions, so he never hits rock bottom and seeks help.
There's a lot of strength in your posts btw, about how it isn't your job to make him seek help, how angry you are about the money etc. You can do this. You can leave.
You might not feel he is actively harming his children. But they are missing all the normal interactions a father who isn't drunk would give them that show that he is interested in their lives, that he cares about them. And you are both modelling how relationships work, what women should put up with, etc. And they know how unhappy you are, even if they never mention it and you think you hide it well. Instinctively they know all is not right in their world, and they may well think that it is them that is not right because we are programmed to trust that our parents are right.
Even if they weren't suffering. You are, you are a human being who shouldn't have to live like this. You deserve to be free. I think you know that. Ending the relationship is the right thing, for ALL of you.
The refrain here (and it may well have come from AA or similar) is that you didn't cause it, you can't control it and you can't cure it.
(this is a fairly long and rambling post - many apologies, I tend to do that and there was so much in your posts to respond to, I doubt I've done it perfectly :) ).