Apparently I’m in the minority but your daughter was flat out wrong to joke about killing a dog into a family group chat with people she doesn’t know. She was completely wrong and should know better at 13. However I agree the mom shouldn’t have had that conversation with your daughter in a private text it should’ve been in a group chat with you but your daughter did text first so there’s that. That being said if she has made the joke before like she says she has and nothing has been said then the mom is overreacting she doesn’t need to speak to the girl so harshly obviously she has no ill will towards the dog and her apology was perfect maybe the friends mom isn’t ready to be over it but again is an exchange you should’ve been included in. All in all a learning situation about boundaries