I like that you are spending a day or two at each location once you arrive. As others have noted, I would also recommend getting a campsite in or near Zion rather than "commute". Watchman would be my first choice. The Virgin "River" runs by the campground and kids of all ages enjoy playing in the shallow water beneath the huge cottonwood trees (unless it's spring and the flow is high). Once you park, you can take the shuttle into the park (your only option) and into town and not put any miles on your RV.
You don't mention the size of the Class C you are renting, but if you are comfortable with driving it by the seventh day, might I suggest taking UT 24 south off of I-70 through Hanksville, then UT 12 through Boulder to Bryce. This will give you a brief glimpse of Capitol Reef NP. This route will also take you through a small (and maybe most scenic) portion of the Grand-Staircase Escalante NM. Otherworldly scenery south of Boulder. Adds maybe 20 miles and an hour to the drive, although with all the photo stops you'll make, it will be a long and glorious day.