As far as I know, the engine battery is separate from the two coach's batteries. The engine's alternator charges your engine battery whereas your coach has a battery charger that charges the batteries via shore power or generator. You must have something going on other than just the LP detector drawing power from the batteries. If you kill the switch by the door, it isolates the batteries from everything. I would just leave it on and plug into shore power and you shouldn't have any problems. Not sure why your engine battery is dead though.
2014 Georgetown 351DS
-TruCenter -Front/Rear CHF -Hellwig Links -Tiger Trak -Ran McNally GPS -ScanGauge -Truck Systems TPMS -5 Star Tune