From Pensacola to Yellowstone would be five hard days of driving at the minimum. Would be better to take a week.
But here is the route I'd take: Pensacola across I-10/I-12 in Louisiana (Not with the floods today!) then I-49 up to Shreveport.
I-20 West to US 69 near Tyler and up to US 82 at Sherman, TX. Follow US 82 to Wichita Falls, TX and US 287 to Amarillo.
Amarillo to Dalhart, TX; Dalhart to Raton, NM and I-25 North to Cheyenne. Then west to Laramie and US 287 to Moran, WY.
That's enough for now. I will come back on later and post possible overnights along this route.
