Personally, I would not try to do over 1200 miles with out spending the night on the road with little children in the vehicle. I think the chance for an accident because of parent fatigue is just to great going 18 hours of driving time. IMHO, the chance of the driver falling a sleep at the wheel while the other parent is napping is just to great a risk to take with those precious little cargos
Carlsbad Caverns does not allow strollers and they recommend baby backpacks. .
Your kids might enjoy
White Sands National Monument. My children at any age loved playing in the dunes.
Capitan, New Mexico is the home of
Smokey the Bear. Not worth going out of your way for, but neat if you are in the area.
Utahtea