I'm one of those who know what limited vacation time is and I'm going to agree while you can get to all of those places, you won't be able to see any of them. I've managed two long trips while my kids were younger and pushed it to the limit while seeing things.
You need at least two nights at each stop to give you a day to see anything besides the parking lots or a hundred feet of the trail. One day, you will lose 1/2 day doing laundary and restocking on food.
While the roads in Yellowstone may be open, that doesn't mean the trails to the sites will be because they could still have a few feet of snow on them. You should see how they break the roads open with dozers pulling road grades and huge snow blowers to remove the snow.
You also missed such places as Badlands (1 night), Rushmoore (2 nights min) as you have Rushmoore, Custer SP, Wind Cave, and Iron Mtn Road (not with RV), Devils Tower (then on to Buffalo for the night), Cody (1 night to restock, take in the rodeo), Yellowstone (3 nights min). Now that's 8 nights right there, so no way you have enough time left for getting all the way down to Grand Canyon. Add a night to Yellowstone, two nights in Tetons, and a night or two heading back to drop off the RV.