I would take in Sequoia National Park (drive through, going south, if the road allows),
but omit Death Valley. It will not be amenable to any of you in the heat of the summer.
Las Vegas won't impress the kids much since they aren't old enough, but an overnight with a drive up and down the strip might get their attention.
you can pass up the Arches, too (imo)
Olympic Park was not that impressive to me, after seeing Glacier and the Tetons, etc.
The Redwoods, on the other hand, were very impressive to me when I was 15.
Yosemite can be done in one, long day. Sequoia is good for driving through and stopping to see the biggest, etc. but I don't know if you can take your rig on the road. It's been a long time since we were there and we were in a jeep, so no problem for us.
Grand Canyon is not open to camping yet, but you can see a lot of it on a tour, in one, long day.
The Tetons offer a spectacular ski lift ride, and white water rafting. Gros Ventre campground has water and a dump station and restrooms and is close to Jackson for a "shootout" on the square and shopping and restocking your groceries at Albertsons.
Yellowstone will take you at least two full days, one for the south "loop" and one for the north. We like to plan on lunch or dinner at the Snow Lodge when we take in Old Faithful. Decent buffet style.
At Glacier, we like staying on the east side of the Park where it's more open to the view of the mountains.
Hope you get to make the trip. It's one your kids will remember all their lives, even if they gripe about the lack of internet service LOL