I don't have kids that age yet, but I can tell you, I remember what I was like as a teen and I don't think I'd let my kids take a long over-night trip like that until they're off to college.
While long distances are a scary consideration, it's the maturity factor and reasons for the trips (circumstances) that would be more concerning to me.
The trips your daughter and her friends are interested in are frivolous, and seem like they will be ripe for more potentially bad things to go down than good.
The whole idea of 3 teen girls staying overnight for a concert would have me wondering who how do these girls interact with each other without parental supervision? Are they giddy and boy crazy? Do they drive recklessly for kicks? If the car is yours - will it return in good condition? If something happens, will there be a liability to me insurance or legally speaking? Will there be access alcohol or drugs (yes, even at a Taylor Swift concert!) Will they be meeting up with boys/men? And if so, are these people that I know are trustworthy? (No boy is trustworthy" when there is a hotel involved). Do they know what to do if they have a car break-down or stranger trouble on the road or at a strange hotel? Do they know how to conduct themselves so they won't look like naive targets to predators?
If she were going on a 5 hour trip with her future room-mate to move into her dorm, that's one thing. The trip has a purpose. There will be a concrete plan that involves preparing for school...moving into a new home... getting aquainted with school and so on.
Their mindset, while probably giddy at the prospect of "freedom" would be "purposeful" and far better than what one would expect with a pack of freedom-starved girls looking for an excuse to have the car, stay overnight in the big city, and to do who knows what into the wee hours of the night in a strange, big city? Afterall, other than the concert, what else could they do for fun that's legal age-wise? And there is no guarantee they'd even stay at the concert. I know my friends and I probably wouldn't if we had a car, and permission to stay overnight somewhere far from home. We'd be exploring and looking for "action" where ever we could get away with it! Testing limits would be our goal in that cirucmstance.
There's also the added "instigator" factor. Your daughter is not going on this trip alone. She will be with 3 of her girlfriends, aka "partners-in-crime," all who are probably looking to benefit from your generous donation of a car and possibly the weekend accommodations. While she may be responsible 98 percent of the time, without your influence, the 3 amigas are definitely going to be more of a "bad influence" when it comes to decision making. Once again, this goes back to the "what's the value of this sort of excursion?"
So, to answer your question, how to cope in the future...for me it is as simple as this: As long as she (child) is in the house, she's still under your watch. Right now, she is still more of a child than an adult and now is the time she needs to learn now that trips and get aways are serious business, even for adults. You set the example by teaching her or leading her to evaluate her reasons for the trips, and what she hopes to gain from them. If necessary, explain your concerns in a clear and reasonable way.
Remember, if there is no valid reason or benefit to a long-distance trip, then why go? This stance has nothing to do with curtailing freedom, over-sheltering them, or not giving them enough responsibility. It has to do with teaching them how to be responsible when they're away from you. Teaching them to evaluate whether or not something that may seem fun is really all that fun, safe or even worth it is empowering and a valuable life-skill.
Talk honestly about why you've made the choice you did to keep her home this weekend, and why with future trips like this, even the trip to Disney probably won't happen on your watch. Afterall, until she's fully on her own and out of the house, and it's her name on the car title etc. you as the parent and person paying the insurance who is ultimately responsible for anyone hurt or injured or goes missing while on a trip with your car.
There is plenty of time for "big adventures" when they're older, wiser, and more mature. But while in high school, and for just frivolous fun, I personally would say "no"...whether she's driving or not.
The coping for you, when the time comes, will be knowing you taught her to make wise decisions and to realize with trips, fun and cars comes serious responsibilities. If she needs convincing remind her of the very sad story of Natalie Holloway...a teen girl who went missing on her senior trip in the Caribbean. She nor her friends never imagined a trip that was supposed to be fun and free would end in tragedy and an unsolved mystery.
We live in serious times and the girls need to understand that and learn how to navigate so they will be safe on their own.