A little clarification is needed here.
The reason the trailer battery is not charging properly with the refer on going down the road is NOT the amperage of the alternator!
It's the voltage loss
in the close to 50 feet of wire between the alternator on the TV and the trailer's refrigerator
The TV's alternator charges it's battery at the proper voltage of around 14 volts but every connection and inch of wire between the TV's battery and trailer's battery presents a small voltage loss, add them together and there's not much left by the time it gets to the trailer's battery when you add in the load of 14 amps the refrigerator
takes the voltage in the trailer is reduced considerably.
Chevy trucks up the charge voltage when the load/haul button if equipted is pushed. Some claim that hurts mpg's because of the shifting but my silverado does not shift any differently when the button is pushed. I've also read turning on the head lights
ups the volts too but have not checked that.