And then if DSD still doesn't go - as is the real issue in this thread - he just eats the loss of several thousand?
Yes @rookiemere It wouldn't be a good situation, I grant you. But what you call the real issue is actually a hypothetical situation, based on ONE prior experience 3 years ago. If the OP/her DH asks the girl directly herself, she may really want to come and wouldn't allow her mother cancelling it as much as she can. If they send an email to the mother warning her that if she cancels she'll be liable for the cost, that would be something. But the OP/her DH are trying nothing. It's clear they don't want to ask her and don't want to take her.
Much better for DH to take DSD away for a one to one holiday / break.
That is a good idea @tallduckandhandsome. The OP might not want that to happen though unless the DH can take his other 2 DC away individually.
If the DH pays for his daughter be will also have to either pay half for his other children or put the same into their ISA or he's not treating all his children exactly the same...
I don't agree @Youseethethingis That's not being equitable. The DH would be paying for his daughter to ensure that all the children got to go on holiday with their dad. He just happens to not have to pay for his other 2 children in this instance. It's a gesture to show that she is his child and not the OP's.
If he did this, he wouldn't have to give her spending money when she goes away with her mum; not the same money equivalent as paying for her but it's one way he could reduce his costs for her.
If you're arguing for a very literal definition of treating them all the same, then the DH should fight for 50:50 contact or at least go back to the court to fight for th contact order to include holidays.
The money he pays for a shared experience of a holiday is in some ways compensating for his SD not living with her father, which his other 2 children do. He doesn't pay anything other than spending money for her holidays with her mother, so his cost re the DD going away is far far less than his cost for his 2 children going away, as he'll have paid for them in the past.