It's sad how people can turn on you so quickly.

I have to say, I'm not surprised the parents quickly changed their minds about their daughter flying out to you. It's a big, scary endeavor to do for a young tween to fly out so far away to visit a friend. It seems they were enthusiastic about it at first, but gave it a second thought and quickly decided no-go.

Then when you sent harsh words, they quickly turned off to you.

I'd suggest you try not to let this incident between the parents end the long-distance friendship between your daughter and her friend. Just step out of it, and let your daughter keep in touch with theirs.