"We met in my town, lived together here for three years, then moved over to his town supposedly on a temporary basis three years ago when his brother was ill. "
So even if everything in your marriage was just peachy, it was never intended to be a permanent move. You both used to live in your home town, indeed since he lived there between the ages of 18 and 34 I'd be inclined to say it's more of a home to him than his home town - that's how I feel about where I live, over my town of birth. He "has been promising that we can move back for ages, putting me off, and it has gradually turned into shouting at me for not being happy there."
Having lived there aged 18-34, your husband has friends there and you are pretty certain that he "could find a houseshare with people he knows well within a couple of days". You even feel you could find a house there if you went as a couple. You are constantly worrying "that he will quit yet another job", so it's fair to presume he's not particularly attached to the job he has, and that it's a job not a career. And you posted "We know people with jobs going", which suggests he could move to your home town (and HIS town of choice too) and be just fine for housing and work, very quickly.
So, the only reasons that I can see for staying put is that he has found a pub where people allow him to drone on about how clever he is without laughing in his face too obviously. Or, as an alcoholic, he is comfortably accessing a supply and doesn't want to endanger it (pubs that will serve him, you to finance him). Or, as the controlling type, he just gets his kicks from making you miserable.
Staying in his home town is not good for your mental health; you are isolated from your support network of friends and family. He is no support. You NEED support; we all do.
Staying in his home town means you feel you have to home educate your children, but moving to your home town would mean that they could go to a school. You visit your hometown regularly enough that two of the children's closest friends live there - so the transition would be fairly easy for them. And frankly I do not hold with the 'any father is better than no father at all' school of thinking. Being a child's parent patently does not prevent an adult from being harmful to that child. Growing up in a household with a stropping, controlling father and a downtrodden, fearful mother hardly sets the template for a life of fulfilling relationships, does it?
The intention was to move to his home town temporarily. Well three years is plenty. You will not be separating the children from their father, he would be perfectly capable of relocating himself back to the town he chose to live in for SIXTEEN YEARS. The only thing that there would be to keep him in his home town is his alcoholism and his desire to punish you for wresting yourself from his control - in which case, sorry, but fuck him. His choice, not yours.
Please, I cans see from how you write that you have lost all your confidence, but the reasons to move home are so overwhelming and the reasons for staying so negligible - please, please move. It is the right thing to do for you, your children, their wider family. It could even be the right thing for him, to move back to his support network of friends.