Birthday party dillema. What would you do?

Hi, my son is turning 12 this week and wants a sleepover on Saturday. He has a handfull of friends in his school and wants to invite 3 of them. The problem is that he does not want to invite his 4th friend. He says he acts inappropriately and will wreck his sleepover. If the kid finds out he wasn't invited though, I'm afraid he will have his feelings hurt. I'm also friends with his mother and will feel very awkward if she asks me why he wasn't invited. Should I pursuade my son to invite him or just let him decide not to and what do I say to the other mom? What is the right thing to do? If I could be brutally honest I would just tell the mom that her kid is not very well behaved, he picks on my younger son as well but I want to be diplomatic. I hate stuff like this. I've been avoiding her just so she won't ask about any birthday plans. I feel like I'm back in high-school!!! Any advice on this would be helpful!