What ever battery tended you hook up will be feeding the 12VDC power distribution panel and other 12VDC items that connected.
Just be sure not to connect the battery tender in reverse polarity otherwise you may blow some fuses...
I have never really used a battery tender. Since you apparenty since you have 120VAC already available there I would probably plug the 30A SHore Power cable of the fifth wheel into your 120VAC source using a RV30A-15A long adapter and let the the fifth wheel on-board converter/charger unit keep your battery charged up for you.
I have my trailer always plugged into the garage here at home in one of the 120VAC receptacles doing the same thing. We can run all of the lights and other things in the trailer including the air conditioner. Just cant run several high current things at the same time otherwise we end up tripping the garage circuit breaker.
The only downside doing this is if your trailer does not have smart mode tchnology charging then you will want to keep tabs on the battery fluids. Applying 13.6VDC all the time may boil out your battery fluids over time.
Even using your battery tender might do this as well...
Just my thoughts
Roy Ken