-
I'm sorry to do this to you but this situation isn't working for me. I need you to leave at the earliest opportunity while I re-evaluate. I can give you up to X weeks to get yourself sorted
This is the right kind of thing to say, being honest is rarely the wrong thing to be. You can be nice and polite about it but something made up will seem that way, and although you might be trying to save their feelings they'll probably know unless they're completely oblivious and it'll be more awkward than the other option.
Just say "I'm sorry to do this to you but this situation isn't working for me. I need you to leave at the earliest opportunity while I re-evaluate. I can give you up to X weeks to get yourself sorted".
Then there's no uncertainty what you want.