Have you considered asking for another site,perhaps out in the grassy area by tepees? We stayed there for a week in June and we were very pleased with our site which was the same as all sites out in the meadow area. The staff couldn't have been nicer. I'm sorry that has not been your experience. The Cody Museum is a nice walk from RV park and we always rewarded ourselves with a soft serve cone from Dairy Queen on our return.
As to not being that close to Yellowstone-you're correct,it's about 65 miles, but I can tell you that it is 65 miles of beautiful scenery! The East Entrance is our favorite! Hope it all works out for you!