I'm going to agree with Mikayla. He gets to walk in to your house any time he feels like it. He gets to store his stuff in your house, with no enforced deadlines from you.
No wonder he thinks it is still his house - it's because you let him act that way. (Plural "you.")
Yes, he can get a window a/c unit. Or, he can go someplace other than your house with a/c. Yes, there are washer/dryer units specially designed for small spaces. And laundromats.
All those are things he'd have to deal with if you didn't live next door. There is no reason you should be forced to move to prove that to him.
Change the locks, and make other arrangements for pet sitting.
I think, if it was me, I'd pick a date about a month from now, make arrangements for help, and inform him that that is the day you will put all of his stuff on his lawn - rain or shine - and the less stuff of his that is in your house by then, the less junk will be on his lawn that day.
But, as many posters have already said, it's all useless unless your DH commits to it and won't back down.