Take It Easy (and Underground)
Welcome aboard the RoadTrip America Forums!
You've got about 3 solid days worth of driving ahead of you, leaving you 2 days worth of time to intersperse stops, hikes, museums, whatever as you make your way east. If you haven't seen Joshua Tree National Park, make sure to do so as you leave L.A. Entering from the town of Joshua Tree and traversing the park north to south ending up back on I-10 would work best. Two very pleasant venues in the Tucson area are the Arizona-Sonora Desert Museum (more of a zoo than a museum) and Saguaro National Park. East of town, south of Benson are Kartchner Caverns. They may be a bit much for your wife depending on how comfortable she is walking for modestly long distances, but they do offer wheelchairs in which you will have to help her up and down some of the steeper walkways - but well worth it. Next up would be to leave I-10 at Las Cruces and take US-70/US-82 across southern New Mexico past White Sands National Monument to US-285 south, Carlsbad Caverns and on to Fort Stockton and I-10 again. Finally, at 200 miles from Houston, San Antonio deserves a look around as you head on to your new home. Trying to go too much farther north of that general line would add a fair amount to your drive time and cut into your sight seeing time.
AZBuck