This is not a situation for your claws to be retracted. This is a situation for you to be swiping at his fucking head.
Do not let this kind of poison & parental alienation & psychological abuse go unchallenged by you. You need am immediate "emergency" session or two with the child/family counselor. The sooner the better. You need to counter every one of those lies. Your kids may not show it, but he just eviscerated them.
You contact your lawyer immediately & tell him to go for the jugular. This must NEVER fucking happen again. If you can get supervised visits, good. If he can't see the kids at all until he completes a parenting class, better.
My EX engaged in all-out mind fuckery of my kids, and in fact still is. The damage he's done is permanent and will still be coming to the surface for years. DON'T LET THIS HAPPEN TO YOUR KIDS! My first lawyer didn't do ANYthing about this. Not until I got my 2nd lawyer did things slightly improve. Even with the weight of this impressive lawyer (frequent GAL, judge pro temp, superlawyer status), EX still fucked with the kids because that was how he was going to win. But at least with my 2nd lawyer we could document my attempts to protect the children.
Remember, with a narc their ONLY fucking goal is to win, which means to hurt YOU. They do not view people as human. They do not recognize humanity. They do not recognize that they are fucking their children over because they don't "see" the humanity inside their children. Children are ONLY tools. A means to an end.
You keep those claws out, Mama. You sharpen those suckers & paint them bright red.
That's enough links for now, but trust me, I have many more. I also want to add that for narcissists, the one thing they cannot abide is "narcissistic injury". When he was publicly spanked on Wednesday, he suffered a terrible narc injury. All narcs have to retaliate. There is no such thing as learning a lesson, self-reflection, humility, "getting it", deep thought. That doesn't happen. Their only thought is to punish, humiliate & destroy. Again, they don't see children as living souls. Children are only tools to be used to destroy their target.
A guy on YouTube, Sam Vaknin, has some eye-opening videos. Check him out.
There is no co-parenting with a narc. They do not learn. There is no parallel parenting with a narc. There is only re-parenting.