Your tow vehicle charge wire from the front of the vehicle to the trailer is not very big (12 or 14 guage wire). Compare that to the cables attached to the batteries in your truck and trailer, they are quite a bit larger. The larger the wire (cable), can handle more electricity being pushed through them.
The charge line from the TV to the trailer, is probably on a 30 to 40 amp fuse/circuit breaker to boot.
Your TV's alternator is capable of putting out somewhere in the area of 125 to 160 amps & a regulated voltage between 13.8 to 14.2 for proper battery charging (TV battery) which is distributed throughout the TV to run all of its accessories/components (and engine components).
Because the charge line from the TV to the trailer is, as mentioned earlier, much smaller than the battery cables and not as much "power" can flow through it, it can not charge the trailer/coach battery as well nor as fast as the truck battery gets charged.
The charge line charges the trailer/coach battery directly. All 12v power is therefore supplied by the battery (including the refer's inverter). The TV SHOULD be able to MAINTAIN the trailer/coach battery if the refrig. is running as long as the charge line to the trailer is hot. If you have NOTHING on in the trailer while driving, then the TV should in fact be able to charge the battery although slower.
Hope this helps clr's explanation.