You can do that a couple of different ways. you can use the output on the inverter and install some recepticals in the places of your choice, run wire to those, or disconnect that TV circuit from the braker panel, run that to your output. And sense you need a breaker for the inverter anyway, run another wire from the braker you disconnected and run that to your input. I don't have a inverter/charger combo, I only have a inverter and seperate converter charger. So, I would have to see what you have on the inverter if it's the same electrical hookups as just the inverter. Can you put the diagram on here?
Sorry, I wrote this really fast as I'm still at work