You'll need an interposing relay that has a 120VAC coil, and a normally closed (N.C.) contact. The relay needs to be rated for the max amperage that you plan on drawing from the battery.
Stick the relay inline between the battery connection on the converter and the battery itself. Wire the coil of the relay to any one of the circuit breakers on the converter.
When plugged in to shore power, the relay will be energized, opening the contact and isolating the battery. The converter's DC output will power the trailer. Your gel charger would now be charging the battery.
When unplugged from shore power, the de-energized relay contact would be closed and the battery would now be powering the lights/fridge/water...
