Yellowstone was the first trip we made with our 5th wheel. Of course from WA it is much closer. Did it with 2 7 year old's and the hardest part was all the driving. Yellowstone is not a walking park, it is a driving park. So, one thing for sure, if your kids are not OK crammed in the back seat together, they will be even less OK after days and days of sitting in the back seat.
But, some points. We actually booked our camp spots inside the park about 4 months before the trip, even before we bought the RV. Yellowstone books up as soon as the sites open to book, so book now if you can. We ended up going over the 4th of July because it was the only days we could get a spot. Imagine taking 7 year old boys to Yellowstone on the 4th - that was their year without fireworks... I guess they will always remember the trip...
We ended up buying a used 5th wheel, bunk house. That was the best, the kids can be in the bunk area playing, watching TV, whatever and the wife and I can enjoy time on the couch, etc. 2 bedrooms is the best with kids. I watched all kinds of people with motor homes try to navigate Yellowstone, set up camp in the evening, sleep, wake up, tear down camp and go travel the day to whatever, then come back and do it all over again. I know you said, rent a car when you get there, but to the best of my knowledge there is not a place in the park to rent. So, you have to go to Cody, Bozemen, somewhere to get a car. Have you booked it already? Something you probably need to book a year in advance, or 9 months or something.
Since you have the truck, the trailer makes more sense to me. Unless you plan to rent or buy a large class A, I think you will find the class C very small with 3 kids. If they were 5 years younger or something, probably not as bad. As a kid we did Yellowstone and stayed in the cabins. It was great, although I hear that the cabins are very old now and not in great shape. But might be easier given the trip you want to take.
I think you said the rental is expensive for 3 weeks. You might be able to buy a great used 5th wheel for a little more money then have it for a few years. You have the truck, so a toy hauler or large bunk house could be very reasonable given your looking at something about 10 years old. You might be surprised, the one we found looks new for the most part and was supper clean. Most people only use their RV's a few weekends a year, maybe 5? So, if they were clean people that took care of their stuff, then it should be in great shape. Don't buy one that someone lived in or full timed in and it should be hardly worn.
Good Luck
