12 volt question!!

[Sdgood1]

OK, Power flush fixed!! broken vacuum breaker under bathroom sink!!!
We took our first short trip in our new to us 2014 3150RL. Almost everything went great!! Here's the question. The TV, DVD, surround sound are located in the rear DS. Wanting to be able to run these items off of 12V so I don't have to run genset all the time, when i want to watc TV. There is NOT a cigarette lighter access anywhere in the area. So in my infinite wisdom figured I could pull 12V power that is going to the puck light over computer desk, hard wired in a 500 watt inverter to run all these items (190 watts combined) Worked great until I tried it without being plugged in for a short period of time (on trip of course) it seems that the inverter is shutting down on low voltage?? Guessing maybe end of line and voltage has dropped that low?? Made sure nothing else on that circuit was on, etc. Should I just go ahead and run a dedicated wire ????? I'm sure somebody else here has tried the same thing. ALL advice appreciated.
The TV and DVD player in bedroom works off a 100 watt cigarette lighter inverter with no problem (only 85 watts) ??????????