Hello, I'm from El Paso..never been to Yuma, but the I-10 highway from Phoenix/Tucson to El Paso is relatively flat. There are a few hills now and then. About 90 miles east of El Paso on US62/180 you'll run into the Guadalupe Mountains and probably the steepest grade in your journey.
I don't know the grade of the highway there, but it's two lanes driving up. So there's no worries of holding people back. The climb is 2-4miles in length (more or less). Once past that it's a slight downhill to the Caverns (about another 40miles away).
Have you visited Kartchner Caverns by Benson,AZ?? I've never been, just passed them on the way to Tombstone. Might be worth a slight detour on the way to Carlsbad.
I tow with a PSD 6.0L as well.