Looks like a pretty good plan considering your time/schedule. You may want to consider hitting Grand Canyon first then going to the Utah parks You will definitely run into traffic and crowds for your stops at wind caves and Badlands due to the rally. Campsite prices will also be hiked up significantly there. I''d suggest reservations for those stops in particular.
The horse ride at Bryce is actually a mule ride and is a great way to see the lower sections of the canyon.
At Arches, if you go hiking, get out early and try to be back by noon or there abouts. You mentioned 4x4. I highly recommend taking the Hell's revenge tour. It's a drive it yourself 4x4 tour and it's a blast.
T-REX 4x4 Off-Road Tours | You Get To Drive | Hell's Revenge>>Moab Utah | Tourist Information | Tours | Rentals | Activities | Attractions | Vacation | Rafting
Also in Moab is a great jet boat ride.
Moab Jett - Colorado River Jetboat Tours - Moab, Utah
You will get wet, but that's great during the heat of the day.
Regarding reservations .n Zion , we stayed at Zion River Resort- it was booked full every night we were there so I'd recommend reservations made in advance. For Bryce, we stayed at ruby's and there was plenty of room in the new section. At Arches/Moab we stayed at Portal RV- again there were several vacant spots. For Yellowstone, if you want to be in the park with hookups, Fishing Bridge is your only option and book now. If you are ok with being on the outside and since you are planning on coming from Grand Teton, West Yellowstone has several parks just outside the park entrance.
You'll have a great time.