" and she not get on mom’s nerves."
I knew there was a catch. Always read the fine print…
^Ha, I was about to quote the same line! That would be hard for my k ids to manage for more than a few weeks.
Your house, your rules. If you don’t think it’s a good reason, then it’s not.
Sounds self-entitled to me, a not so great character of this generation. Please, no offense meant to any particular person here. One of the best gifts you can give your children is independence and knowing how to live within their means. Now, a young twenty something should have lots of spare time to work an extra job if that first one doesn’t afford them some of the luxuries they want. Too often I see kids with a better car, better phone, better shoes…than the ones I’m driving, using, wearing. These same kids are complaining that they can’t afford rent, vacations, or health insurance. That’s a problem.
My kids were told they had to move out Labor Day after high school…they could go to college and thereby maintain a place/room in the household, get their own apartment, join the military…their choice, but staying home, working non-career jobs, sleeping in at their leisure and the other teenage privileges, was not an option. My son did ask if he could stay home and start a business. I would have said yes IF that business was not seasonal, so the answer was no. They both know they can come home for any emergency reason including health, loss of housing no fault of their own, short term to save for a down payment, that sort of thing.
My answer would be get a second or third job to finance your travel.
I think it totally depends upon the family situation, the relationship, the people involved, finances, so many variables. It’s hard for people to weigh in on this specifically, because we are all biased towards how it would work for us.
Magnetron’s daughter could move in with me, she sounds great 
We have some friends who are renting an entire house, and they sublet out the bottom floor. The daughter graduated from college, and they let her rent out that floor, with another person. So she got a good deal, and they got a pleasant tenant that wasn’t partying and smoking pot like the last one. Win/win.
I think as stated that it comes down to how resourceful her daughter is. There are tons of ways to take a European trip that are affordable. They just might not be staying at a 5 star hotel doing it.
One of the best lessons my husband taught our kids was how to create and maintain a budget on a spreadsheet. From that they could see where their money was going and how to set their spending priorities according to their goals. Both have been out of the house and on their own since graduating and so far, so good. We did let them know that if they ever moved back into our area, they were always welcome to live at home for a little while to save some money.
At some point, independence from parental purse-strings, living within your means, is far more important as priority-lesson than expensive travel opportunities. Said adult-child would benefit from gentle redirection, to focus on the good fortune she has attained, rather than look to parents’ home as route to more vacation travel. A key goal is to not be governed in life by “keeping up w/the Jones” mentality, to be satisfied w/what you have.
I agree with @lilmom. If we as parents have taught our kids how to budget, then hopefully we can be supportive of their plans. That said, it doesn’t mean we have to enable financial plans we don’t support- but that is an individual choice.
If either of my s’s he wanted to live home (neither did, even when one lived in town for a year when working here) we’d have let them do so and probably would not have charged rent, but we would probably leave that open to discussion if (a) they were not doing their share of the household responsibilities and (b) they were being cavalier with their disposable income. We would support a reasonable savings plan, but would not likely feel comfortable if they were not being adult in their responsibilities/choices. Yes I am being general in my use of terms as I have no specifics at the moment as to what we would deem unreasonable or irresponsible as it is a nonissue. and I am just musing, but we would have a conversation that we would expect an open dialog and expectation that we would revisit the arrangement if need be.
DS#2 made some financial choices at one point that we were not totally on board with, but he sent DH graphs and spreadsheets and used an online budget app (Mint, IIRC) and never touched his work salary money. It was IMO. more risky than I was comfortable with at the time, but he demonstrated his success. Its still a bit out of my comfort zone but its his life and his $.