Effy, we're trying to help you here...really! :)
Without knowing the exact locations you want to visit, putting a round trip of North Carolina, Tampa, Nashville, Tempe, California, Grand Canyon and North Carolina into GoogleMaps says it's about 6,500 miles. Even if you could drive 10 hours per day averaging 50 mph, that is still about 13 days of driving.
In your original post you said you have 2 weeks, maybe 3 due to your job. Which is it? If 2 weeks, I think you'll see that just won't work. If 3 weeks, then you will have just about 8 days for visiting family & attractions along the way. Of coure, this assumes there are no "bumps" in the RV road such as mechanical issues which require attention, etc.
When I do my planning, I use the 50 mph average while travelling to get us into approximate locations. For extended trips, I will group these along the way and IF we have a mechanical issue that might eat up 1, 2 or 3 days, then I look at destinations we might have to skip to compensate for the lost time. A good part of your trip is along a fairly straight line, so you'd probably have to forgo your last destination, CA. But that might also be one of your most important. (My wife wants us to see the Redwoods too. She's A LOT more excited about seeing them than the rest of the family, but I KNOW if we travel out that, if we DON'T see them, it will be a VERY COLD trip back and that cold will linger for a long, long time! LOL)
The other thing I try to do is plan for full out travel to our furthest destination, and then pick spots to visit on our way back home. In this way, we're always working our way back home after the initial push. I realize on a long trip like this, it might not be possible, and you have that Tampa detour which will eat up 2 or 3 days, but again, laying out the KEY places to visit is paramount, and then fill in the others.
When you're travelling on the road. Are you comfortable staying at Walmarts/Flying J's/Rest Areas/etc. or do you prefer campgrounds. My preference is Walmarts, and after 3 days on the road I'll look for a Flying J's for a night to dump the tanks and take on water. We just did this on a recent trip to Florida via PA (Hershey Park Winter Event), Atlanta GA (Six Flags Winter Event) and ultimately Fort Wilderness in Orlando. Anyway, again, something to think about. If you're going to be travelling late, you probably don't want to be arriving at a campground in the dark. In my opinion THE WORST part of RVing is arriving in an unknown campground at night. Plus, the campers already there aren't usually too keen about late arrivals. So, we use Walmarts quite commonly.
Good Luck,
~Rick