Since you're avid hikers, I'd suggest Bryce, for sure. It a cooler park in summer because of elevation and the trails are like a fairy wonderland. The kids (and you) would really enjoy it.
Then take Hwy 12 up to Capitol Reef Nat'l Park - more great trails.
If you have time on your return, stop for a few days at Moab for Arches Nat'l Park. Again, the trails are awesome, especially the Fiery Furnace range-led hike. Again, the kids would absolutely love it. If you only have a couple days for Moab, concentrate on Arches NP rather than Canyonlands. The hikes are more fun.
Personally, I'd skip Zion for this trip and instead, do the above three parks.