I have same model inverter as you. There is a transfer switch within it. If your front TV works with inverter,the only other powered outlets should be as Bill Davis describes. The NRV drawing for 120V ac circuits also show that to be correct.
The wiring diagram shows a duplex receptacle in the electrical bay just forward of the entry door. In mine, the ac output from the inverter is wired into a knockout in that duplex box and becomes the branch feed for the rear bed tv and vanity. From there it feeds the front entertainment center.The front TV power is relay switched via ignition switch to prevent front TV operation while driving.
I added a larger inverter and more batteries to provide all outlets with inverter power excluding water heater and a/cs
Marty
Try plugging in a 60 watt lamp at the rear bedroom outlet. The TV there may not like the output wave form of the inverter.