We sort of made that same trip two years ago! We were on our way to our first work camping job in Moran, WY; about 10 miles from Colter Bay. However, we attended an RV Safety Conference in Colorado Springs and went up and through Yellowstone first. Therefore our trip took us from DFW area west on US-287 to Amarillo then I-40 to Albuquerque, NM. Headed north from there on I-25 all the way to Casper, WY. In Casper, we headed west and north on US-20 through Thermopolis and Greybull, WY. and west to Yellowstone. This past October, we returned from Moran, WY. via US-26/287 through Lander and Rawlins, WY. to I-80. Depending what you are driving/pulling and how confident you are with up and down grades, the main highways may be easier to travel. Most of the trip from Albuquerque to Cheyenne will be up and down (mostly up) but I-25 is a beautiful drive. US-26/287 is extremely beautiful and as you apex Togwotee Pass the Tetons will be in your front window all the way to Colter Bay! Safe Travels and Good Luck.
NRVIA Certified RV Inspector #523
2003 Monaco LaPalma 36DBD - 2013 Honda Fit