I agree that a van is a good option. Cargo (and passenger) vans often are quite capable tow vehicles with decent payload ratings, unlike many SUVs and some pickup trucks.
A motorhome would be another reasonable option. In the event of a breakdown, you can run the roof air conditioner from the generator without needing the vehicle to be operational. Of course, that doesn't work too well if your "breakdown" is running out of gas. A motorhome also won't heat up as quickly in the sun as a car. In terms of repair service availability, it's true that there are more auto garages around, but repair facilities for larger vehicles are not extraordinarily rare either. A class C motorhome (built on a stretched van chassis) will be a bit easier to get repaired than a class A, though probably not by a huge margin.
Chassis problems are relatively rare if you have reasonable preventative maintenance--things like making sure the brakes are in good order, etc. More common are difficulties with the house parts of an RV, most of which needn't bring a trip to an immediate halt. A malfunctioning interior light or even a dead fridge isn't the end of the world.
Some campgrounds may not permit you to camp with all your animals.
