You may not like it, but he IS their father and he has as much right to the kids as you do. You don't have to like everything he does. However, as long as he is not drinking and driving with the kids in the car, he's not doing drugs and not endangering them in any way, you have to let him have his time with them too, regardless of what you think his intentions are (using them for 'show').
I see nothing wrong with him keeping them over night as long as he isn't endangering them in any way.
If you really feel they will need a bath ask him to bring them home before 11 so you can do that.
As was mentioned, make sure you have the custody agreement in your divorce papers so this is all worked out fairly for both of you.
Believe me, I was married to someone who didn't want anything to do with the kids. He even asked my new husband to adopt them, which he did. Now the ex still wants to see them on his 'other' kids' birthdays, just to make it look good. But, ya know what? I let them go (they are old enough to decide for themselves now if they want to go or not).
Just remember, when your kids get older they will form their own opinion of their father. Do not do anything to influence them either way about him, it will only come back to bite you in the end if you do.
Kids are smart and they know who it is that takes care of them and who provides for them. They know who it is that takes care of them when they are sick, who goes to their school for things, etc. They won't forget it.
They will also figure out who is being 'fake' with them and who is real with them.
one thing I always did for myself was to never make a promise to my kids that I didn't/couldn't keep. If I wasn't sure, I told them I'd try, but didn't promise.
If I ever say "I promise" they know I WILL follow through, no matter what.
you see, their dad always made promises and never kept them, so I made sure when I made a promise, it was kept.
Good luck, I hope you and your kids have a wonderful holiday.