I don't think that most RV's have a large enough battery bank or charging capacity to run a fridge on 12V for long. It might be OK for maintaining a cold fridge for short periods of time.
When we had our old Toyota Class C, we never operated the fridge on anything but propane. It hardly uses any gas at all for the fridge and the stove. We turned on the water heater before dinner and turned it off after the dishes and showers were done. There was always enough hot water for the breakfast and lunch dishes. No reason to run the water heater longer as it heats up very quickly. We had an 18# built in tank and could run 3+ weeks on a fill.
Of course if we ran the furnace gas would only last a weekend.
We drove a lot through the mountains and never had any issues with the fridge being off level while traveling. If we stopped and could not find a level spot to park, we turned the fridge off until we got going again. We follow the same routine with the TT.