I would venture a guess that dropping a car off at the North Rim will be impossible, since there’s virtually nothing there, certainly no rental agencies that I’m aware of — how would you get there without a car in the first place?
Some alternatives, neither of them cheap:
Note that both shuttles are seasonal and operate only May to October.
All in all, you’d probably be best off altering your itinerary to meet your daughters at the South Rim, Flagstaff or Williams instead.
Credit:stackoverflow.com‘