I've driven I-10 west from Deming to Tucson numerous times in my old gasser MH pulling a Wrangler and it isn't too bad. There are a couple long pulls but nothing that slowed us to less that 45-50 mph.
An interesting place along the way to stop is Bowie, AZ, which is a mostly dried up/almost new ghost town. Turn north at the post office and about a half block later you will see the store, the one that sells the goodies from the nut groves and vinyards you see along the interstate. Try to stay away from their home made fudge as it is way too good to the taste buds, especially the praline fudge.
The west side of town has a (run down) RV park with w/s/e in pull through sites for $15/night. The guy that owns it is from the old school, maybe even from before the school was there. Heck, he may even be one of the original AZ settlers from 18xx for all I know. DW and I stayed there coming and going a few times and we always had good service and felt safe.