“It’s her daughter that’s costing her a relationship.”
Yeah, but the OP is the experienced adult in the situation and she’s the one who can see how dangerous it is.
Yes, that’s true.
Also, it’s somewhat age appropriate for a young 20-something to be more loyal to her friends (and I count Cousin George as a friend) as compared to close relatives. I remember myself at that age, and I had very similar behavior toward older relatives. 1) I was detaching from them in favor of friends nearer my own age but 2) I wasn’t yet totally financially independent and 3) I had a tendency to expect older relatives to treat my friends or pay for good causes I was involved with. I wasn’t a bad person or an especially immature 21-year-old, but I did need to learn that generosity means being generous with my money, not other people’s money and that meant I needed to make my money.
This is a lesson that needs to be taught, but it needs to be taught gently to preserve the relationship with the daughter.
Thank you for this perspective on it. I did find it interesting she was stressing over and over to me how MUCH money $200 is, while apparently not realizing that $1600, total cost of the trip, is quite a bit more. And missing the realization that she, her cousin, and friend, all continue to live rent free with their $200 while I have monthly bills, 7 kids to feed, and a major driveway repair ($4K) this summer with my $1600. Perhaps part of the teaching is discussing that with her kindly.
“Next time she wants something, she’ll go to her father. He’ll be the nice guy and give whatever she wants, because he likes always being the Good Parent. If she pays him back, it will be proof in their minds that he did things right and See, no problems between us. If she doesn’t, he’ll let it go and continue doing whatever she wants at his own expense so he can be the favored parent, go more deeply into debt, because he really can’t afford it, and they’ll all take the attitude that it’s my fault he’s in such bad financial shape because I’m the ‘greedy *****’ who’s now ‘holding grudges’ and blaming her for her cousin’s decision.”
Have you pointed out to your daughter that her father is in very poor financial shape?
No. It’s never come up. I’m sure she hears it from the other kids because he lets
them know and they worry about it amongst themselves. However, in typical fashion, it’s often blamed on me–for ‘stealing’ his money (ie, child support, he pays no alimony), or for divorcing him at all. (The truth is, he was so deeply in debt, behind my back, I believe we would have lost the house sooner or later. By making a legal break, I have made sure I can continue to provide a home for these kids when his house of credit cards collapses.)
I’m just afraid that surrounded by so much family dysfunction, you’re now in shoot-first-ask-questions-later mode.
Possible.

It becomes very difficult, perhaps impossible, to really deal with these things well when she and her cousin are almost certainly being backed up by their relatives.
If your daughter is still exactly like this four years from now, I think that could be evidence of poor character, but for the moment, nothing that you’ve mentioned that she’s done or said is unusual for a young woman her age.
Overall, she’s really doing well for her age and taken on a great deal of responsibility for herself. She has rarely asked for money except in major emergencies (for example, she lived in Manhattan during Sandy and there was a lot of stress and upheaval as she lost her home and had to be re-located–two or three times–at the same time she was taking GREs for graduate school.)
She is actually the only one of the four legal adults who
did pitch in during the trip. I believe she actually bought a meal or two for her friend and cousin, and I did wonder that they stood around letting her buy for them, too. She is also the only one of the four who pitched in without being asked to help with the planning and organizing beforehand–which was a major job in itself.