Here are some example itineraries that you could modify to fill a longer time (these are 11 day tours). (DesertHawk has given you so many places to go it would take all summer!)
http://utah.com/itinerary/grand-circle-tourhttp://www.americansouthwest.net/itineraries/grand-circle.htmlHowever, these tours mostly cover the desert parks. I'd take part of the trip into SW CO and visit Mesa Verde, Durango (don't miss the Durango-Silverton Narrow Gauge RR - one of the most scenic places in the country), Ouray, up to Grand Junction and over to Moab from there. This area is higher elevation and much cooler in the summer, giving you some relief from the heat of the desert. At some CG's, you'll find yourself needing a sweater in the evenings!
As far as places to stay, in Zion I'd strongly urge you to stay at Watchman CG in the park. Electric hookups only, but the Virgin "River" (really a stream) flows right by the CG and is used by many kids to wade, build little dams to make pools, etc. Nice shade under the cottonwood trees, too.
One nice thing about Bryce Canyon NP is the higher elevation and cooler temps. But don't try to stay at one park (or between them) and visit the other - too much driving.
Trailer Village IN Grand Canyon NP is the place to stay. Park once and use the shuttle to get around the south rim. Also higher up so a little cooler.
Although it can be quite hot, I'd still recommend a few days in the Moab area. Do your hiking early in the day and find some place cooler in the heat of the afternoon. The trails to the various arches in Arches NP are just a great time for kids. Do try to hike out of the Devils Garden parking lot. Lots of arches to find. For afternoon activities, a raft trip down the CO river might be fun for your kids. Hike up Negro Bill Canyon which is in shade for much of the day and thus cooler. Or take a drive up to the LaSal Mountain outside of town to see the red rock country from above. Take some food, have a snack and watch the sunset from up there. We love the Moab area and usually spend nearly a month there every year if you add up all of our trips.
I think Arches and Zion NP's are the most fun for kids, although Mesa Verde is quite good for your two older ones. The train ride is also something kids love. Plus, Silverton is a real, honest-to-goodness old west mining town with wooden sidewalks and dirt streets.
As far as heading to the coast, I think I'd spend all my time in the four corners area. It's quite a haul to the coast and once you're there, it's very crowded. Between the deserts, the canyons, Indian ruins, and the high mountains, the experiences your kids will have in the four corners area will definitely keep them excited and interested for the whole time (as long as you don't spend too many long days driving).