I have been going to Yellowstone since 1955. A great place to visit, but the two best times are May and early June for the babies, and Sept and Oct for the elk rut.
The cooler wetter weather makes the Park less attractive to the seething hordes of people. In an RV you have a nice warm place to sleep at night. Be ready for some cooler weather and rain. It might snow a little at night, but will go off quickly.
The wildlife is actually much easier to see in cooler wetter weather. You will get to see all the babies, especially the little red buffalo calves romping all over the place.