If you've waded through the
Charging While Towing thread in Electrical Secrets, then you may know me as the wacko who
charges his trailer battery by running a smart charger from a 12V inverter fed by the TV. The main reason for doing it this way is that the charging system in your TV is tailored to quickly recharging the starting battery, and won't necessarily supply healthful voltages and currents to my (your) fancy specialty deep cycle battery.
A lot has been written about battery charging, discharging and storage, and written by people more knowledgeable than I am. The main point to remember is that one charging method does NOT fit all. For longest battery life use a charger suitable for your battery.
Here's a quick run through my current (pun intended) charging while towing system.
It all starts at the TV battery:

another view:

12 volts from the battery goes through a fuse (red wire) to what looks like an old school starter solenoid. That's the shiny object off in the darkness that my fingers are pointing to. This is a
Cole Hersee (24059-BP) 12V Insulated SPST Continuous Duty Solenoid. It is controlled by the yellow wire, which is hooked up to a wire that is hot only when the car key is in the run position. Thanks to the solenoid, there is no connection between the TV battery and the trailer when the TV is turned off. When the TV is turned on, the solenoid connects the red wire to (can't hardly see it) the 10 ga black wire that runs back to the 7-pin plug at the tow hitch, shown here:

The connectors at the front of the trailer plugs into the TV's connectors.

Note the large white, black and blue wires coming out of the 7-pin plug. these are ground, +12VDC and electric brakes. There's also a small red wire peeking out of the bundle that is the backup light wire. I kept the 4-wire pigtail so that the trailer could be towed by any vehicle with a 4-pin plug. I hook up both plugs to tow and charge.
In the tongue box, the white and black wires connect to a 400W inverter:

110VAC comes out of the inverter through the yellow plug, and enters the trailer through this junction box:

where they go to the back of the trailer and power the smart charger:

(the gray "Genius" box, upper left under the counter).
At the risk of overloading you with too much information, the power for the charger enters the trailer's system through this relay setup,

which allows me to plug into shore power without having to remember to throw a switch or something. The charger plugs in here.
Just for fun, another view of the wiring nightmare under the galley:
