hi hope, well, it's not a very good situation to be in and I'm sorry you are. It does happen though and there are some things you can do to make your life better.
We have a big row in the morning, he makes the promises and then has one weekend off the drink, declares he doesn’t have a problem & we’re right back to it.
This is a waste of your time and energy. He will quit drinking the moment he wants to and not before. You didn't Cause it, can't Control it and can't Cure it (the 3 c's). What are you boundaries around this. If you won't live with a person with a drinking problem then you won't. If that is your boundary, then he will have to move. Boundaries are for you, not him, they are completely within your power.
he just doesn’t want to go back. I think he thinks if he just hangs around, I’ll eventually forgive him.
No he probably doesn't want to, but that's a bit beside the point. You aren't willing to live with a drinker, he isn't willing to quit, you are at an impasse. He may not want to go camp at his parents house but that may well be what needs to happen.
There is a saying around here - you don't set yourself on fire to keep someone else warm.