You're young and energetic. You've been on some long-ish trips already, so you have some idea what you are getting into. Ok, fine, go for it. But stay flexible in case you have a problem, get a whim, have a sick kiddo, grow weary of the heat, whatever. Don't be married to the itinerary. If you find that you'd rather go a different direction in the middle of the trip, just do it. Even if you have to break a non-refundable reservation, it's worthwhile doing so in order to keep the vacation a fun one.
I would add a drive through (and hike in) Colorado National Monument. Not quite as spectacular as Arches, but very worthwhile... and not quite as hot. There's a nice state park by Fruita, just north of the monument, as well as a CG in the monument itself.
Speaking of heat, Arches is likely to be oppressively hot from noon to 7 pm in summer, and be mindful of the road work they're doing in Arches this year. Plenty of RV parks around Moab, mostly pricey, but you want the electric hookup for the A/C. Portal RV Resort sits a bit farther off the highway than most so it has less road noise.
Bryce Canyon and the north rim of Grand Canyon are about 8000 feet so the temps are more tolerable. In Bryce, most people stay at Ruby's Inn, but I camped about 10 miles west of the park at Red Canyon NF CG. Be sure to hike some of the trails at Red Canyon, especially the Arches Trail. There's a paved bike path parallel to the highway, too. At GC north rim, I boondocked on NF land a dozen miles north of the canyon; there are tons of back roads you could explore by driving or hiking, and the scenic rim trail heading south from Point Imperial could keep you plenty busy depending on how far you want to hike it.
Zion is another hot location where you'll want to arrange most of the strenuous hikes for early am and late pm, although the Narrows hike is cool all day. If you have bikes, take 'em and coast most of the way from Sinawava on down... a great way to catch a breeze without working up a sweat.