In my truck and Hawk, there are "were" two 30 amp auto reset breakers on the 12 volt line on each end. I had problems with the one on the camper side continually tripping and resetting (it was faulty). If your camper battery with the refrigerator on (or off) pulls over 30 amps, it is possible for these breakers to keep breaking and resetting. This may be why mine went bad. I added #6 wire to the existing wire between the truck and camper and changed out my breakers to a different solution. They are manual reset breakers now so I need to pay attention to them. But more often than not, I drive to my destination with my 3 way fridge powered by the battery. One of these days, I will arrive at camp and forget to switch it back. I just hope there is plenty of sun to charge my camper, when it happens.
Since, weather permitting, I can probably go two weeks on a tank of propane, I am not saving much by powering the refrigerator with the battery while traveling. But I enjoy doing it. I have two 79 amp hour batteries. And a 130 amp solar panel.
If your camper is set up anything like mine, you might want to be concerned about having those 30 amp thermal breakers start tripping and resetting. And, of course, forgetting to switch back to propane at your destination. For example, if you stopped along your trip and did some shopping for 45 minutes. You truck may be able to deliver over 30 amps to the camper when you start off again. 30 amps was the charge limit in my camper before the breakers would start tripping.
I have a 100 amp alternator in the truck. I am not sure just how much current it could supply to the camper.
Steve