Florida to Yellowstone, Grand Teton, Grand Canyon and back

The Yellowstone and Grand Teton parks can take week to ten days to explore. Three weeks really isn't enough time to see all three parks. I plotted a route in Mapquest using Tampa as a starting point since you didn't say where you were staring. The Mapquest mileage was 2330 miles just to Yellowstone. If you average 60 mph it's over 38 hours of driving. You may want to rethink your plans to something less ambitious.