3 week trip from Atlanta to Yellowstone

3 weeks does seem like an acceptable timeframe to do YNP & the Tetons from GA, and still have enough time to hit the highlights and enjoy them. I'd suggest spending 3-4 full days (i.e. 4-5 nights) for Yellowstone and 1-2 full days for the Tetons. You could hit the Black Hills on the way there and perhaps Bryce on the way back, though I think I'd suggest something with a little less driving to get to - from West Yellowstone you could come down I-15 through SLC (stay overnight), then take I-15 to US 6 east to Green River, Utah, spend 2-3 nights there (there's a KOA and also a state park, both with some shade - it will be hot!) and take day trips to Arches and Canyonlands NPs and Dead Horse Point SP. From Green River you can head east on I-70 and have a beautiful drive through Colorado. (Not easy on the vehicle due to the altitude & climb, but all interstate so no winding & twisting.)

For Yellowstone, definitely stay at Grizzly RV Park. Great base camp for a rig your size, and since you have a toad, you're all set to visit the park. You can do a day trip to the Tetons & Jackson from there, but it will be a long day; you might consider a night or two at Colter Bay RV Park (if you need hookups) or at Colter Bay or Gros Ventre CGs (no hookups) and be by/close to the Tetons.