A lot of the messages come across as if they've read the original post, not the follow-ups referring to the anxiety. Seems to be an important point i.e. it's not about being a sore loser or a spoiled brat or overprotective mum.
However, I'm not sure why DD agreed to the RPS if it's that important to her - it makes the issue seem like a game to her/that she's happy with the 50/50 chance of getting the seat or not.
Why is the DD so interested in having the seat, yet he's willing to forego it for cash? Seems a bit odd when it's his daughter rather than mate down the pub.
Is this a joke that's getting out of hand or does DH not take the anxiety seriously? Does he think the DD's reasons really are due to the anxiety, or rather that the anxiety has been brought up because the game didn't go her way (i.e. they sound like reasons most people don't want the middle seat).
They could both have been accommodated, of course- window seat for DD, middle seat for mum, then DD in the window seat in front or behind.
I'm an adult but still holiday with parents - mum always wants the aisle seat, I want the window seat. Dad also wants the window seat but will settle for the middle seat on the basis that he'll be uncomfortable wherever he sits, but at least in that configuration the rest of us will get a chance of some sleep /easy access to the bathroom as preferred. Better to have 1 person uncomfortable rather than 3 uncomfortable and unhappy.