What a delightful story. I am delighted how it worked out. This is what Customer Service is all about. Fear of flying is a very real thing and not fully appreciated IMHO. I think that a lot of the drinking that goes on aboard stems from this. Whilst I totally disapprove and detest drunks, I am certain that this phobia has a lot to answer for.
I do have one question - OP do you think that your daughter's fear of flying has been somewhat abated? I do hope so.