Lee, you can do as you suggest. One thing to be certain of, is that if you do use the fridge
on DC, to turn it off when the tow vehicle is not running, as it will drain the batteries very fast.
If the trip is a short one, I don't bother powering the fridge
at all, as it will hold the heat out quite good if the door is not opened a lot.
When traveling long distances, I usually just light
burner on the fridge
. I am not sure about all the states in the US, but everywhere in Canada it is allowed, with the exception of posted places, like on ferries, or some fuel stations.