It depends on the individual kid.
It does sound from your wording that she is your step-daughter - if so, that could make things a bit more awkward for you to be saying no and your wife saying yes. Best to find a way for your wife and you to be on the same side.
Maybe suggest a "breaking in period" of X number of years before it goes out on loan. You and your wife put all that money into a new RV and it doesn't make sense for others to enjoy that newness instead.
Maybe blame the husband/boyfriend's carelessness, etc. That takes the daughter out of the argument - it's not her, it's HIM. And wife will be more likely to accept a derogatory comment about him than her own daughter.
Maybe suggest a few family trips with all of you instead. Then you can see first hand how they behave around the RV, as well as how well they take care of their own gear and yours. Show them all the work that has to be done before leaving, while you're there, and when you get home (really, think of all those things you can point out MUST be done - inspecting all the canvas before and after each trip, checking all seams, and so on - things that will make the idea of borrowing it less appealing to them).