Personally, I have a hard time getting excited about NM. To me it's mainly a state to be driven through to reach CO, UT or AZ. (Apologies to NM lovers.)
Red Canyon is just east of Bryce Canyon and is worth a couple of hours at least; the arches trail is great. From Bryce, I'd suggest taking Hwy 12 north over the shoulder of Boulder Mountain; there are spots where you can see for miles and miles. Drive through Capitol Reef, then north on Hwy 95 and turn off to Goblin Valley SP; I guarantee your kids will love walking around the giant sandstone "goblins" (they look more like giant mushrooms to me) and playing hide & seek in the crevices at the campground. There is a narrow slot canyon just a few miles north and west of the SP, I've read, if you want to hike one of those. Then head to Arches.
Arches NP is one of my favorites. If you like Arches, you'd probably like the CO National Monument near Grand Junction. More great sandstone features and spectacular views. Definitely worth a half day at least, and good camping either in the park or at the SP closer to town.
The drive north through the SLC area is very scenic, with mountain views. The family might like to stretch their legs by clambering around City of Rocks near the southern border of ID.
Since you are from OR, have you ever been to Wallowa Lake SP? I've seen photos, and they make me want to go there.