Oh, Sarah, I feel for you! What a situation! I think a lot depends on whose idea it was for XH to stay at your house. If your AC asked for this, as Anne believes, then, yes, they should take some responsibility for telling him it's time to leave. If he asked you, then, it's totally between you and him. You own the house - it's up to you who gets to stay there and how long, and, basically, up to you to enforce it.
Even if your AC did ask for XH to stay in the house, it may be hard for them to kick him out. He's their dad, after all, and they, no doubt, still love him even though you don't and despite his faults. So, in the end, if you really want him out, I'm afraid it's going to be up to you, regardless.
I know you don't want to be the "bad guy." But how is asserting your rights over your home being bad? It's not as if he doesn't have anywhere to go. You agreed he could stay for the celebration, not move in permanently.
But he has always been a user and taken advantage of people, etc. (probably b/c of his addictions). You knew that. So I could be wrong, but I think you let him stay out of guilt that you couldn't be there.
No need to feel guilty though. As PPs have pointed out, your AC (and SIL) still depend on you - and XH leaned on you for years (and is doing so again, now). And there's no bad guy - unless it's XH for taking advantage of your generosity. You're just a home-owner asserting her rights over a home she alone pays for, etc.
What are you going to do when you lose the flat at the end of the summer? Go back to living with the man you divorced? Giving him room and board and a nice, clean home as you did all those years before? I hope not.
And why shouldn't you be able to happily go home now? Why are you paying for everything, yet the only one who can't comfortably live in the house? IMO, this has to stop!
I think you've been given a lot of good suggestions for getting him out. Please use whatever strikes a chord with you and do it. As a PP said, you don't have to give a reason - it's your house, period.
To change metaphors, please take the bull by the horns, get him out of your home, and don't let him back in again for any reason, no matter who asks.
Best of luck and please let us know what you decide to do and how it pans out!