We use a small crock pot while traveling down the road. It is a one quart model by Rival and is rated at 75 watts (as stamped on the bottom of the unit). We place it in the sink, so it is secured and when we arrive after a long drive, we have a nice pot of pinto beans, or a pot roast or similar fare, hot and ready to eat.
To the OP, there should be no reason not to use a crock pot with similar power as ours on your inverter while driving. As others have suggested, I would operate the fridge on LP while on the road. We do and believe it was designed to be operated in that manner.
