I'm in the minority too. I see nothing wrong with an adult (who is almost completely dependant upon her parents financially) being asked to pay for a portion of a vacation. Several comments on the topic:
Mom & Dad are paying almost everything for this student: room, board, transportation, and some school expenses. What does that leave? Partial school expenses, which she's "paying" through loans. So she's working 10 hours per week to pay for incidentals such as meals with friends, clothes, haircuts . . . typical college student stuff. 10 hours isn't much; her work plus her studying combined probably doesn't equal 40 hours.
So, if she WANTS to save $200 for an airline ticket, she can probably do it. She may need to skip a new outfit and an outing with friends (don't we as adults have to make similar choices?). Or she may need to pick up some extra hours at work. But all her NEEDS are met by her parents and the loans, so she won't go hungry because she bought this ticket.
For some reason, Dad thinks she needs more financial responsibility. He lives with her, so he knows her habits. Perhaps he's irritated that she's spending on tanning sessions while he's paying more for her health insurance, perhpas he's noticed that her car is getting old and she isn't putting anything aside towards a downpayment on a new one, perhaps he just thinks "it's time" -- who knows? If Dad has an inkling little feeling that she "should" be doing more financially, he's probably right.
In general, I think parents are doing too much for their teen and adult children these days; as a society, we're turning out some spoiled young adults who don't know how to "make do" on less, who don't appreciate anything other than the best, and who use credit cards rather than save. Is this true of this young lady? I don't know, but I know that kids who don't learn financial responsibility at a young age almost always end up paying dearly once they're out on their own. Anyone ever read The Millionaire Next Door? The theme is interesting: The author has ample research showing that the most successful people generally had to "make it on their own" after high school.
My parents enforced that philosophy, largely because they were barely getting by themselves -- like another poster's parents, my parents had been given everything as teens and young adults, and they didn't become "financial adults' until late in life; because they have no retirement, I'll probably be supporting my mother at some time in the future. Because they weren't able to help us, they made it clear that once we were out of high school we were expected to pay our own way 100%. We were allowed to live at home (huge house, big family farm), but we had to pay a token amount towards the household expenses and we were responsible for work around the farm. They were not able to pay anything towards our college educations, but we did qualify for some financial aid. I worked really, really hard to get through college, but I graduated with honors and two degrees. The financial lessons I learned were valuable; I'm not 40 yet, but I live in a paid-for house, drive a paid-for car, don't owe a penny to anyone, and have money in the bank. For my own children, I'm striving for a mid-way point. I am more able to provide than my parents were, but I also want them to adopt frugal ways so that they'll be able to live within their means as adults. I suspect the original poster is coming at this question with similar motives.
Back to the original poster . . . here's the big problem: If the girl doesn't pay for her ticket, Dad intends to pay for it himself. She's been living in this house for more than two decades, and she probably knows this. So she loses nothing by "playing Dad's heartstrings". I think that since Dad's already said, "Pay it yourself", he should stick to it.
I think most people are coming at this from a fairness issue -- the girl is a family member, even if she is legally an adult. I don't think there are any hard and fast "rules" on whether a college student "should" be included in family vacations. In the long run, teaching financial responsibility is much more important than being fair, and it's certainly more important than any vacation.
So . . . is it right to have the girl pay for her own ticket? I think so.