It would help if you added your year and model of your Montana to your profile. I am assuming you have one of the newer Montanas with an integrated inverter. I understand it powers the entertainment center, and plugs in the kitchen and bathroom, and optionally a household refer.
I would be using the inverted outlets in the entertainment center for your TV and VCR (really - a VCR and not a DVD?).
You say they added the additional inverter by your TV. I bet they used an existing 12V DC wire in the area to power the inverter rather than dragging a new 12V line. Given the distance from the batteries to the TV the standard wiring is too small for the current needs of the inverter. Bigger 12V wiring is required. The inverter is complying about the lack of voltage it is seeing to current loss over the long distance. Plus the power needed by a VCR is a question. It by itself may be more than the capability of the inverter.
Carl (n Susan)
There is more to life than fuel mileage.
2012 Montana 3700RL Big Sky Package towed by a 2015 Ford F350 6.7L PSD 4WD CC LWB