One more thing to consider is some rigs have power management systems that shut down systems in order of importance based on how much power is being supplied. Now, that doesn't explain the "furnace" (which is probably propane with a DC control board)... unless you mean an electric heat pump. As for the fridge, if it's AC or propane, I can certainly see how the management system would shut down the AC side when, for example, the batteries are low and all of the available power is going to the charger... or a cycling electric water heater, for example. 110volts is not much for a coach... assuming you're even getting that much, concerning the gauge and length of the cord.