Make your own hammock-style car seat cover. The hammock style keeps the dog from getting hurt if he or she falls during any sudden stops or starts. Get the pattern here.
Dog Travel Accessories; Car Seat, Shopping Cart Cover, Car seat Cover Pattern by Simplicity 2984 TLC's Treasures www.etsy.com/...
Car storage bag. Kids can see everything inside, but all toys and goodies are off the floor.
This would work well for a dog that tries to dart out of the car as soon as you open the door. You can probably do a diy version with a bungee cord, carabiner, and leash.