Most factory alternators are neat maxed out at idle with the lights on and heater fan at max. If you can rev the engine off idle and have ANY change in the battery voltage (other then a momentary blip) the alternator won't be charging anything on the trailer. Now the nearly fully charged TV batteries will be pushing amps to the lower voltage trailer batteries, and the alternator will be pushing a few amps to both, but most of the gain is from the TV batteries, not its alternator. There are aftermarket alternators that put out several times stock at idle, and full power. I have a mean green 240 amp in my truck. It is rated for over 100 amps at idle. Once the glow plugs cycle off it is pegged at ~14.4 volts.
