You mentioned a Pure Sine inverter GOOD. NEVER get one that is not a Pure sine.
There are various ways of attaching the inverter for use in the camper. The easiest way is to get an extension cord or electrical wire, and run the plug from the inverter to a NEW receptacle. Or if you have two plugs on the inverter, run two separate NEW receptacles.
NEVER EVER wire the inverter directly into the campers existing 110v plugs unless you take precautions.
I have a 2k pure sine inverter, which I initially had 2 separate plugs for (it has a remote on off button). I got fancy and wired it into my campers main. Things I must remember are to turn off the campers converter, the and the AC. When the inverter is on, everything (including microwave) runs perfectly, except the AC.
Get a device called 'Kill a Watt' available at Harbor freight, or Lowes, Or HD. its about $20. This will measure how much juice your TVs, charger, etc needs. That way you will know the inverter/batteries can support it.