OP, I presumed you had both rigs and were trying to decide which.
But you have neither? If so, then IMO the TT is the FAR more economical option. Whether you rent or buy a trailer, it’s cheaper than a C by a long shot and anything you get is hook n go behind a F350. No special setups or expenses there.
Kids would vote C all day long and twice on Sunday. It’s a nice option but factor in renting cars a couple times as you wish to, it is even more expensive.
Trip there n back, flip a coin. I don’t mind towing. Some do, but if you don’t then no issue there.
If you only have a couple/few main destinations and will drop the camper for days at a time, then the TT makes sense to me. If you will be moving locations every day or 2 then the C is easier to pick up and move.
Good luck, great trip planned! We did similar a couple years ago with the kids. 3 weeks, MT fishing, Yellowstone, Rushmore, a week back home in WI and back to WA. Seemed relaxing enough to me.... 1900 mi home = 2 long days drive. No biggie.
