I don't know if you got your question answered or not. Running the propane furnace in your trailer when plugged into the house 120VAC will be just fine. The propane has no connection to your house 120VAC.
The propane 12VDC furnace blower however will run from the converter/charger unit and/or the trailer battery. The 120VAC connection to the house will run your converter/charger unit when plugged in and will also keep your battery charged. This will be you only connection concerning the propane furnace.
The propane furnace will put out the most heat for you but you will have to live with the loud BRRRR sound of the furnace blower motor. Also the propane furnace will be consuming your propane tanks big time.
What everyone is telling you if you can get enough heat from the Electric Heaters you might want to just run them when connected at home. This is what we do here... I do have my propane furnace turned on but with a low thermostat setting so that makes the furnace a back-up source of heat in the event it gets below the thermostat setting during the night.
The only downside wit using the 15A/20A 120VAC from the house is you have to watch what is turned ON at the same time. The Electric heaters draw is pretty high to start off with and it may trip the house breaker if other high wattage items are turned on at the same time. i.e. running one electric heater and a couple of lights may trip your house breaker if the furnace blower unit kicks in. You will have to experiment with this...
Just my thoughts...
Roy Ken
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS