Ok his post made absolute sense to me. Very clear no confusion. I will reword
He wants to know if he can install a 1000 to 1200 watt inverter to power an outlet or two, either existing transferred to the inverter or added so he can run a TV and perhaps a coffee maker.
To the OP the answer is yes.. I will give you two methods
First common to both the inverter needs to be close to the batteries, BUT It does NOT need to breath fumes from the battery which can be corrosive.. I suggest the compartment next to the batteries (or just behind them on some trailers).
For an inverter of the size you wish the recommended MINIMUM is a pair of GC-2 (200+ amp hours at 12 volts) I recommend 2x that.
I also recommend PURE SINE WAVE over MSW, and this goes multiple for TV use.
Now the two Actually 3 ways
Inverters in teh 1000+ range come in two flavors
One is a "Stand Alone" this converts 12vdc to 120 VAC only For this type of inverter I would suggest you run wires from the inverter. IF it has circuit breakers on the 120 volt side (one or two) you can just run from it to an outlet or two. One near the TV, one the kitchen,, Make them a "Contrasting color" (Actually Red/Orange is suggested for Inverter power) to indicate these are 'Live" full time.
The other kind is an "In-line.
This type often has a charger internal as well and can charge the batteries Often this is a good quality 3-or 4 stage charger.
For a 1000 watt (For 2000 watt use a 30 amp breaker) 20 amp breaker in your MAIN box 12 ga to the inverter's 120IN and if the unit has breakers 12 amp you can use 12 or 14ga to the outlets
NOTE: if hte inverter does NOT have internal breakers you run 12ga to a "Sub panel" and two breakers there one for Kitchen one for TV 15 amp.
NOTE: The "Third" method is to use a stand alone with an auto transfer switch
In this case a 15 amp feed (12 or 14ga) to the GENERATOR input on the ATS and feed the inverter (Also via a breaker) to the SHORE in output goes to the outlets
Or use a manual switch
Make sure the inverter output is breaker protected.