I would not recommend staying in the center of these three National Parks and making day trips to each (if that is what you are asking). They are way, way too far apart. Even if you were visiting the North Rim of the Canyon, it's still way too far from Zion. You really need to stay close to each Park. The South Rim of Grand Canyon has a campground with full hook-ups. Zion has a campground in the park that doesn't have sewer at the sites, but the location is terrific (better than waiting in line to enter the park every day). Ruby's at Bryce is about the "only game in town" but does have full hook-ups and is pretty nice. My advice, do yourself a favor and stay in the parks and take the free shuttles. If you don't, you will on your next trip out there...ask me how I know
A side note about an additional overnight stop is at the Best Friends Animal Sanctuary in Kanab, Utah. They have two full hook-up RV sites (they take reservations) and the place is well worth an overnight or two. It's a first class place and if your grandkids love animals, this will probably be the highlight of the entire trip. They can also volunteer for a 1/2 day or 1 day or longer.