Seeing Yellowstone without a reservation booked is almost impossible. During the season, traffic in the park moves at a snails pace, with huge crowds and limited parking.
Putting on a hundred miles and getting out to enjoy little bits of it is a full days undertaking.
Summer camping can be fun, but Walmart camping so you can spend almost all your time on the road just isn't like camping at all. Take the time to find out of the way parks instead of the popular places, relax in wilderness parks, and enjoy your new rig.