Trailer batteries never charge hardly at all from the towing vehicle. The towing vehicle's voltage regulator sees the voltage of the engine compartment battery, and adjusts its voltage based on keeping that battery at ~14.4V. The voltage drops in the wiring (and along the vehicle + trailer frame) create sufficient voltage drops such that the trailer battery is lucky to see 13.8V, at which it takes days of towing to recharge...
The only way to make this work is to put a step-up converter in the trailer. (12 to 13VDC input to make ~14.7V output at ~20A).