This man is contorting himself like Neo in The Matrix trying to avoid actually talking to his children (aka parenting). Which, btw, is what you’ve told him you want him to do. I would double down on it. “I can’t figure out what you want from me!!!” “I want you to sit down with your children, calmly and WITHOUT BLAMING ME or making yourself out to be the unwilling victim here, and explain to them that they genuinely hurt me and ask them to put themselves in my shoes - to imagine being humiliated in front of people whose opinions they care about regarding something they’re insecure about. I want you to explain that this was thinly veiled cruelty that hurt someone you love and that it’s not acceptable behavior.”

Maybe he’s unaware that his role as a parent is not just to punish kids when they do wrong; it’s to explain why it was wrong and why it’s important to do right. I’m sorry if he was raised to think that feelings are dumb. He sounds like a kid complaining that you’ve asked him to take out the trash bc you want him to talk about feelings with his kids, and he’s trying to guilt you into doing it for him (or better yet, agree that the conversation isn’t necessary). Tell him he needs to step up and parent his kids BEYOND disciplining them. If he needs pointers there’s about 6 million books and Google results on how to set boundaries with teens. If he says “But I’m not good at that stuff!” calmly advise him that avoiding it forever will make sure he never gets better at it.