BFL13,
Maybe I missed this in the reading, but when you shut the propane off, do you shut off your refrigerator too? If it's a 120VAC/Propane model, it will probably automatically revert to propane when AC power is disconnected. (Maybe the inverter keeps it running for a while, but during your travel, it reverts to propane?) If the propane valve is shut off, the refer will try to light several times, and as it does, it might use whatever propane is left in the lines until the refer times out and stops trying to light. Then, when you get to your destination, you have to reprime the lines. Possible? Another culprit could the water heater as well, if that's left on.
By the way, we keep our propane on most of the time. The few times I've shut it off to travel (going through tunnels), I made sure all of the other gas appliances were off, and when I turned it back on (later that day), all was well.
As for refueling the rig with gasoline, shutting off the propane doesn't necessarily eliminate a danger of a spark, as the furnace, water heater, refer, etc. will still try to ignite (spark) on gas even if there is no gas present, at least for a little while. This spark could ignite gasoline vapors. Therefore, the APPLIANCES should be shut down before refueling, or at least those which will be near the fuel pumps. That's what I do, I don't worry about the propane tank.
As others have said, there are safety devices which allow the propane to remain on while travelling, but I also understand the situation with your long-term marriage. :) Congratulations, by the way!
Safe travels,
~Rick