What would it take for you to not be threatened by having her stay as a friend?"
Nothing. That door was closed when he put the relationship beyond friends and betrayed your trust. He can never go back. Involving her in any way (especially with your children) is the problem, not the solution.
I'm going to answer your main question, and I'm going to be quite blunt. You need to go into protection phase as soon as possible. Honestly, you should have done it before the holidays. Anything else only reinforces his idea that he can somehow have both. The message you need to be sending is a very strong boundary - you will not be in his life as long as she is. Any wavering of that boundary will only make him more determined to try to ignore it. It will only send him a message that the boundary is weak and negotiable.