Sadly, that is normal. I plan to look into wiring the bedroom tv up to the inverter as well. That is, as soon as it gets out of service. Although Jayco advertises it as a 400 watt inverter, it's actually a 1000 watt unit. It should have the capacity for both.
Brian, Mary, kids, beagle - Moose, and mutt - Maggie.
2012 Greyhawk 31FS
2013 Ford Explorer Toad