I always thought that you weren't supposed to travel with propane flowing through the pipes (i.e. shut off at the tanks). ??? Am I incorrect?
You do not have to shut off the propane tanks while running down the road most of the time. There are some longer tunnels and ferry systems that make you shut off the tanks. Other than that you can leave the propane on and run the fridge off propane while driving. As stated if the fridge is close to the fuel tank fill point it is a good idea to turn off the fridge (but not the tank) while pumping gas. I do this every time since mine are close to each other. Just walk to the fridge hit the off button, pump gas, walk back to the fridge hit the on button, grab a drink and snack for the next leg of the trip and drive off. Obviously the drink and snack is optional.