Steve,
All outlets are not run through the inverter. If the two outlets in question function normally on shore power, but do not function on the inverter while other plugs operate normally on the inverter, they are not powered by the inverter. In my 2000 Marquis, the plug on one side of the bed is powered by the inverter, while the plug on the other side is not.
Normally about 2/3 of your base plugs will be powered by the inverter. You can unplug from shore power, turn on the inverter and take a test light and check all of your plugs, to see which ones are powered by the inverter. If it is important to you to have the nightstand plugs added to the inverter, the average electrician can add them to the inverter in an hour or two. I would suggest that you add them to a ground fault circuit, or create a new ground fault circuit for them.
Gerald