Phil and Cathy, I'm probably not going to be much help for that road report you wanted. While we've driven it many times, we never pulled a trailer on it. Wayne says he doesn't remember the grade being a problem, but then again, we were either in our truck or my Explorer and weren't dragging an RV behind us. I do remember how "on the edge" some of the road was on the way out--no room for drifting off to the right or left in spots! I can tell you that the RV's are bumper to bumper along it, everything from pop-ups to monster Class A's, so if the grade is a problem, we've never seen evidence of it. We don't remember seeing anyone pulled off with brake or overheating problems, ever. However, you might call the National Park Service for an accurate assessment: 307-344-2117 (for Yellowstone road info). That road is busy--along with normal tourist traffic, all the huge delivery trucks, etc., travel it regularly bringing in supplies.
If you haven't visited that site Bob gave you for Yellowstone information, you should do so. It's a great place to check current road conditions among a multitude of other things:
http://www.nps.gov/yell/. I noticed there's a link on the site that takes you to an updated road map, and there's also a link for current road conditions (which was pretty interesting because of some road work and/or other conditions that are affecting some of the park roads temporarily).
We've never stayed in Valley View RV Park, but we have friends who have, and they said it is a great place in a great location. Because most of our RV traveling up to now has been to the west of Yellowstone, I know nothing about the other parks you mentioned. (Boy, we wish we were headed to Goshen for the fall rally--lucky people!)
Oh--the advice some other MOCers gave you is spot on--visit the Teton National Park first. It has gorgeous vistas. But when you see Yellowstone, you'll be blown away. I'd hate to see Yellowstone first and then be expected to be that excited over the Tetons, too! Teton National Park pales in comparison.
Carolyn