Drained battery

[skcin]

That's because the outlets need 120 volt AC to power them. Your trailer does not have an INVERTER that changes the 12 volt DC power from a battery to 120 volt AC power. It has a CONVERTER which converts 120 volt AC power to 12 volt DC power as well as supplying 120 volt AC to the outlets in the trailer.

 
Also batteries are limited in the amount of amps they contain. Inverter work by sing large amounts of 12 volt amps to supply small amounts of 120 volt amps. That 1200 watt Mr Coffee drip coffee maker that only uses apx 10 amps on a 120 volt outlet from shore power will draw apx 100 amps from the battery while it makes your coffee when using an inverter.
It's the old watts = amps X volts.

Good.  Now I know not to worry.  Unfortunately, now I have to tell my husband that he was right.