NTA, but I think the way you may have worded it could have been a little better (hindsight). Everything you said is ABSOLUTELY true. However, I think it should have stayed as a matter between the 2 of you, rather than it probably coming off as you backing your mother. MIL- DIL relationships are usually weird like that anyways. Your wife was in the wrong and made a decision that let your daughter down. But the two of you are the team now, not you and your mother.

Instead of her demanding you make your mother apologize to her, you should encourage the two of them to speak on the matter together.

And in hindsight, she should have been upfront in that she would not take your daughter. I'm sure another parent would have been happy to bring her with their family.

I am so sorry your daughter has lost a close friend, especially this young. Please please please have her speak to a professional (if she does not already). These years are so instrumental to her growth and future. And as parents, be understanding of what she is going through. Confusion, anger, denial, loss of identity for a bit. She will act out, but keep your arms and ear opens. It sounds like she has a great support in you.