What part of the country are you in? Are you going to be staying put or traveling? The easiest way to stay cool in a mobile environment is to drive somewhere that's cooler. But that's not an option for everyone either.
As you found out, air conditioning is not real practical off grid. You can however run a powerful 12v fan off grid, and I suggest everyone have one! Fantastic Fan is a great brand. You can move 900 cubic feet per minute, which is more than enough to exchange the air inside your vehicle with outside air. That means you can keep the inside about the same temperature as the outside.
Obviously in areas like the southwest where sun is intense, sun is your biggest enemy when trying to stay cool. Park in the shade whenever possible. Some people even build platforms on roof racks (e.g., plywood painted white) to keep the sun from beating directly on the roof of the vehicle. Of course, keep in mind if you're charging with solar you can't shade your panels and keep your batteries happy at the same time.
The other issue with pets in vehicles is that even if you've taken all the precautions (leave plenty of water out, fan exhausting hot air, window open for fresh air...) you still may get that conscientious do-gooder who sees your vehicle and takes it upon himself to smash a window or call the cops. Just something to be aware of.
