Agree with what the other responders have said. I've driven from Colorado to Alabama and back many times (family in Tuscaloosa area), and without towing it's a hard 2 day drive (12 hours per day), and towing, it's a good 3 day drive. Adding one more day to get to NW Wyoming adds another day...just of driving. So, plan on 8 days minimum for driving, unless you really want to push and/or swap out drivers.
As far as places to stay and things to see along the way, you'd need to really settle on a route to get there for advice. There will likely be all sorts of suggestions for the best routes, whether to take interstates or secondary/US highways. Figure roughly 1800 miles one way, give or take, depending on which way you go.