A very aggressive itinerary you have there.
While the highways and by-ways of the Eastern US can be beautiful and meeting minglers can be enriching you are missing out on a lot of beautiful interesting things by stay on the highways.
For instance:
Roanoke became a city so quickly that it earned the nickname "Magic City." The Mill Mountain Star, also known as the Roanoke Star, is the world's second largest illuminated man-made star, constructed in 1949 at the top of Mill Mountain in Roanoke, Virginia.
One of history's greatest unsolved mysteries: what happened to the lost colony of Roanoke Island? Founded in August 1585 by Queen Elizabeth I's favorite, Sir Walter Ralegh, the first English settlement in the New World was found abandoned without a trace of the colonists in 1590.
The Great Smoky Mountains (Cherokee) are a mountain range rising along the Tennessee–North Carolina border in the southeastern United States. They are a subrange of the Appalachian Mountains, and form part of the Blue Ridge Physiographic Province.
From Tennessee to Wyoming there are many attractions and significant points of interest you will miss out seeing/experiencing with such a fast itinerary.
I assume you are taking I70 across to Denver then north at Denver to Wyoming?
Nashville has the Country Music Hall of Fame and many music oriented shops near it. Dollywood and the Great Smoky Mountain National park is just south east of Knoxville and Douglas Lake is just east of Knoxville.
At the 40/55 interchange is Memphis which has Elvis shrines and you can do the Lively "Street Crawl" along Beale Street in Memphis. Great food and live music.
The Cahokia Mounds State Historic Site is the site of a pre-Columbian Native American city directly across the Mississippi River from modern St. Louis, Missouri. You can also visit Trail of Tears, Lake Wappapello (rent a cabin), Johnson Shut-Ins and Elephant Rocks. In St Louis you can go up in the Arch or take a lazy riverboat tour on the Mississippi, Lots of Bald Eagles and falcons. You can see Mark Twain's cabin at Mark Twain lake.
St Louis Zoo is free, there's also a science center and amphitheater.
In Kansas City the Lakeside Nature Center is beautiful in the spring. Plus there's the Kauffman Memorial Gardens.
Sadly, I found most of I70 pretty boring in Kansas but when you see the Rockies come into view it is beautiful. You'll notice the colors of the dirt change.
Sadly, I've only been to Denver so I only experienced a small part of the Rockies but what I did explore was breathtaking.
Drive safe, make sure you take lots of pictures and video, you will want them.