I definitely agree with playing things down and avoiding drama, I have thankfully reared two girls that have had drama free friendships so far🙏.
However, it doesn't appear to be a few girls from what the OP has written.
I'm reading it that it was a largish group and if the girls are sharing a dance class, and another hobby, for which they travel together, it is not surprising that she might hope to be included.
I have read that it is the OP that is doing the lifts, not a shared arrangement?
This child is happy enough to be regularly in her company accepting other invitations.
She has invited school friends and some dance friends, and the daughter isn't close enough to be included, which is fine.
But chatting about it in front of others, particularly a child that she shares another hobby with, is transported there with, and also regularly goes on other outings with, is not nice IMO.
I know my girls wouldn't do it.
If the two girls didn't share lifts and regular outings there would be no issue whatsoever, as they are just part of a dancing class and friends from it.
The girl has made her decision at 12 and it is very reasonable for the OP to revisit exactly how involved they wish to be with her going forward.
Giving endlessly is not a good basis for friendships/relationships and certainly not what I would encourage in my daughters.
As a parent I think it is quite possible to be breezy about things like this, whilst at the same time saying it's ok to be disappointed.
I wouldn't encourage my daughter to deny her upset as if she is wrong to have those feelings, far better to explore them and ask her if they really are that close and encourage her to focus on friendships where she will be included in occasions like this.