No 12v operation ( three way operation ) on newer RV fridges. 110 & propane only.
Some coaches factory wired with a dedicated inverter to supply 110 to the fridge while the engine is running. If your seeing damage, you may want to consider this as an upgrade.
Always had Dometic fridges in my 5 RVs and never had issues using propane in motion.
EDIT: The fridge should hold temp for 4 hours with no problem in normal temps. then you could start the gen set to cool, even when on the road.