We stayed in Gardiner in July, though not with our RV. I don’t recall seeing Rocky Mountain, but did see Yellowstone RV Park. It didn’t look bad, and I wouldn’t hesitate to stay there, especially for convenient access to Yellowstone.
As mentioned, Yellowstone’s edge is quite a distance from Yellowstone’s entrance. When we passed it, I remember thinking “almost there”! A half hour later we finally made it.
Gardiner is pretty convenient for stocking up on supplies, gas, and has plenty of restaurants to choose from. Nothing fancy at all, but reasonably priced.
Enjoy your trip!