Is your fireplace a Dimplex? ...does it look like this
If so, I don't believe it has a remote. I have one in another RV and the controls are located in the bottom panel.
Pull at the very top of the bottom panel and the panel door which is hinged at the bottom will drop down and enclosed in that panel will be all the controls you need.
At the left is the on-and-off switch and knobs which will increase/decrease the lighting intensity of the flame and the other knob will increase/decrease the motion of the flame.
At the right will be the on/off switch for the fan. There will also be a knob for the thermostatically controlled fan.
Here is the owner's manual
for it if it's a Dimplex BF8000ST as we have in an RV. The control panel that I mentioned is shown (illustrated) on page 10 - Figure 6.
I'll let others answer your question to the TV plug issue.
And, we are thinking of buying a Forest River park trailer so I'm going to be asking questions on this forum eventually. Maybe you can help me out on some of the questions I'll have.