I'm sorry that happened, I can actually understand his reaction. That is a pretty strong accusation on her part and he is right that there could be legal ramifications for him. Also for you, of course. If she decides to spread this venom around CPS could get involved.
Regardless of what he does, your number one priority is the protection of your children.
Personally? I would seek out a lawyer. If you can't afford one you could contact a low cost legal aid group for assistance perhaps. I would ask them what can be done, perhaps even a temporary restraining order but I would get their recommendation.
She is playing with fire here with total disregard for you and your children and your boyfriend.
I am sorry about him breaking up with you. Perhaps when things have cooled down a bit you will be able to talk this through? Also, you need to protect him and getting legal advice shows your commitment to do this.
It may not be enough for him but is still the right thing to do perhaps.