Check the voltage at the camper battery when the truck is off, then start the truck and check. If the voltage goes up you are charging. If not then you are not. (Don't plug in 110 for this test).
On my truck it needed a fuse so that the circuit became live. $2 and I had a pack of them.
Never run the fridge on 12V for any length of time. I would use 110 to cool it off at home, switch to propane when I pulled out of the driveway and off propane when I got back in the driveway from the trip. Most campgrounds I stayed at did not have power. Yes off when refueling as well.