In two weeks, you will only be able to hit the highlights of a Western swing through AZ, UT, and CO. I realize your kids are a little too mature for the "Cars" movie franchise, but a fun 15-minute stop along I-40 in Arizona is the 1950-vintage Wigwam Motel in Holbrook. It has the full-size concrete teepees with Route 66-era cars out front, just like the movie. And, if you happen to be an "Eagles" fan, a similar short stop in Winslow can be a photo op at the "Standin' on the Corner" statue. After Grand Canyon, I would head to Zion NP via Las Vegas and the new bridge at Hoover Dam. If your kids like to hike, take them on the "wade" through the Narrows, although you now have to get a permit to do the hike.
From Zion, you have a decision to make. Northeast will take you to Bryce Canyon, Capital Reef, and, possibly, Arches NPs, Colorado National Monument, Black Canyon NP, Pikes Peak, and rapidly home on US 50 to US 24 to I-70 (a route that completely avoids Denver traffic). If you decide on this route, don't miss driving spectacular UT 12 between Bryce and Capital Reef. At Capital Reef, the Fruita first come-first served cg is definitely worth getting there early in the day to stay in. And, if the Devils Garden cg at Arches is full, an even more scenic alternative is the electric-only campground at Deadhorse Point State Park on the Island-in-the-Sky portion of Canyonlands NP (just be sure to fill your water tank before going there). Black Canyon NP has electric hookups in their cg, but Colorado National Monument doesn't. If air conditioning is a necessity for maintaining friendly family relations on your trip, stay at the tree-shaded, FHU, James Robb Colorado River State Park cg in Fruita and just drive your toad or TV up the cliff to Colorado NM. And, if you stay on US 50 after Black Canyon, your kids would love a raft trip through Brown's Canyon on the Arkansas River. You can schedule it from either Buena Vista or Salida, depending on the route you want to take home.
Traveling southeast from Zion will take you past the North Rim of the Grand Canyon, Glen Canyon Dam, Monument Valley, Mesa Verde NP, Durango and the train ride, Great Sand Dunes NP (which the kids will love!), Bent's Fort NM, and home on the Santa Fe Trail. If you go this route, I recommend staying at the Juniper CG at McPhee Reservoir/Rec Area near Dolores instead of camping inside Mesa Verde NP. This USFS electric-only campground with paved sites, water, and flush toilets will keep you from having to take your RV up that long grade to the Morefield campground. And be sure to take time to visit the Anasazi Heritage Center next door to Juniper cg. It's the best Anasazi museum in the Four Corners; the kids will love the interactive features designed just for them. They might even learn more about Anasazi culture there than at Mesa Verde. They can even hike up the hill from the museum to a small Anasazi pueblo.
A great adventure for the kids at Mesa Verde NP, now that there is no shuttle service, is to sign up for the Weatherill Mesa bike tour. However, your vehicle must be less than 25 ft long and under 8,000 lbs. (are you pulling a trailer or have a toad?) to use the road into Weatherill. Check it out on the Mesa Verde NP website. If, after Mesa Verde, the kids are not "Anasazi-ed out", you might want to stop at new Chimney Rock NM between Durango and Pagosa Springs for a hike to the top of the mountain. There you can view an Anasazi pueblo located specifically as a once-every-18-years lunar observatory.
Finally, the SE route lets the kids put their hands and feet in 4 different states at the same time at the Four Corners Monument on US 160 SW of Cortez. It's a 15-minute stop/photo op that every teen will want to put on social media for their friends to see.