At I-10 just before getting into the Phoenix mess you might want to consider picking up Hwy 85 south at Buckeye which will take you to I-8 at Gila Bend, AZ then take I-8 east to join up with I-10 again. It avoids a lot of traffic.
If you're ready to stop around Benson, AZ east of Tucson, Kartchner Caverns State Park is about 10 miles south of I-10 and the cave tour is excellent. The adjoining campground has electric.
Deming, NM would be the next place to stop after leaving Benson. The museum is awesome... a little of everything and very well done. Lots of RV parks in Deming.
Then you'll be fresh to tackle driving through ElPaso, preferable on a Sunday morning.