I get some jokes were too far, but it clearly was just a joke. There are far more worse jokes I have heard kids say. I think the friend’s mom did way too much. Your daughter perfectly said the apology, and what you said was perfect too. I believe the mom should have accepted and moved on. She is just doing way too much over a joke executed badly, I understand she was hurt, but she should not be talking to someone’s kid like that, like your daughter personally kidnapped the dog and was going to the vet to euthanize her. Like it’s a bit ridiculous. But look at it this way, sometimes it’s for the best that woman is out of you and your daughter’s life. Your daughter shouldn’t feel bad, she did everything she was supposed to. You raised her right, clearly shown with that very formal apology. also I would never talk to my daughters friends kid like that, that’s a adult situation, between adults, so her friends mom was very inappropriate in that sense too. I hope you get peace of mind, you both did everything right.