In a MH one does not have to plan meal stops which helps or bathroom breaks for the kids that age. When we went to YS the kids were turning 14 and did 8000 miles in 31 days so we were able to work in Pacific Ocean and Grand Canyon too.
We left KY at 2pm and got to a WM in NE at 2am and was in Badlands NP by 10pm on second day and toured the park at mid night under full moon and it was SO cool then slept in visitor center parking lot. Did the park again the next morning again before Mount Rushmore and slept in Cody WM parking lot that night. While real life experiences it is a bit much for some.
I started driving a tractor at age 5 so if it has an engine, steering wheel and a seat and is moving I am in hog heaven. :D
With kids 13/15 they will find things to do alone the way as adhoc stops.
We stayed off the interstates for the most part so we ran up on nice little out of the way parks and things. It would give me a chance to get out from behind the wheel (solo driver) and walk around while the kids ran wild for a few minutes.
Of the 31 days I think we spent 9 in hotels because it was cheaper and/or just make more sense based on were we needed to be the next morning. Birthday weekend in Carlsbad CA we stayed in a hotel three days and two of them we walked to the beach so they could learn to surf and on the second day each stood up and surfed into the beach.
We got into YS after lunch and bought bus tour tickets for the next two days (did a loop a day) and after hitting the major stops on south then north loops they said they were finished with YS and to head south. We had NO scheduled plans period as to where we would go and when the trip would end so they did the routing as we rolled. It was a school field trip and I was just the bus driver.
If I were ever go to YS by RV or car I would have reservations at a lodge or CG. In our case we found out SUV/hotels was our cup of tea in part because it is cheaper renting a SUV than driving the MH we own. Now if with my physical limitations I had to move the luggage myself then the MH might win out. :)
Our 31 day wild west MH trip of the life-time cost $8K (not counting MH ownership cost) which gas was $4K of the 8K. I can tell you if it had not been for getting the old MH and working on it for five years we would NOT have taken that trip by car. With an RV you it will help you get out more so I am not anti RV. We use the MH for a backup house and it is nice to go places and park in the drive of family without wrecking their private lives by moving in on them. :)
Jnccpf a 24' C is a great size for moving fast as no toad is required we learned in our 32' A on our trip out west. Being as young as you are you can drive as far as you like because on our trip I was 60 and have severe physical limitations getting around but did hike with the kids some like at Kings Canyon because you have to do the trails to see the Redwood trees the best.
My objective was to get to the far starting point quickly so our first stop was the Badlands which was 1200 miles or the same as to Boston a couple weeks ago by SUV.
Update us with photos after the trip. Have fun and do not ever let dream stealers steal your dreams. Monument Valley and four days with family my kids had never seen or knew were alive in NV were my highlights. I have no regrets pushing myself but do be safe.