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You've got a bit of a problem here. The route you've outlined is about 3600 miles, and with only 7 days to work with, that means you're going to be looking at driving more than 500 miles a day every day. Realistically, if you stick to the interstates and make the minimum of stops, that's going to be 8-10 hours on the road every day. That time also doesn't include the extra time you'll need to visit the places like the Grand Canyon, do things like take a balloon ride, or get off the interstate and take a slower going route like Route 66. To do all of those things, you're going to have to probably make some days even longer.

If you're up for a go-go-go trip, you can make this work, but know, you'll be driving 7-8 hours on your short days on the road. You'll need to have a few days where you'll be on the road for closer to 12-14 hours to fit in the kinds of things you want to do.