wolter, there has a been a lot of controversy over the years about running the fridge on propane, but I think most RVers now do it.......I do now that I have a 2 way fridge instead of the 3 way fridge in my previoius Trailmanor.
As 1 poster stated, you need to turn off the gas when fueling.....which is hard for me to remember so far.
Sme states require propane to be turned off in tunnels......VA. beiing 1 of those. There are inspection stations that you need to pull into, and they will check your gas to be off.......you can turn in off then if you like, or before if you anticipate the tunnel at your last pee stop. I like to do that, so I can walk in the trailer and turn the fridge off before turning the propane off.......just so the fridge won't try to be lighting without propane. You will see campers stopped at the nearest convenient pull-over after tunnel and turning their propane back on.
If you are still concerned about the propane issue, super-cool that puppy during the nite before, and just turn everything off......it should stay cool during travel, as long as you don't open the door. Me, I like to stop for a drink and sandwich during the day.
If you are really inventive, and don't want to travel with the propane on, maybe you could rig up a inverter to run the fridge, but I don't know if the TV charge could keep the battery charged enough for that.