While we are on the road can I leave the house battery on. Also if we're parked in a rest area or Flying J stop should we leave the battery on if we're not running the generator.
Yes and yes. You have to have 12v to operate the fridge, if it's an RV fridge. You shouldn't have to turn the batteries off for a short time, unless you have a draw on the batteries somewhere, but that's another issue.