Clearly something is very wrong in the circuit if the caravan battery is running the car!
Decades ago we had a split charger relay . It only switched on when the engine alternator was running. Engine off ,no power from alternator it switched off.
My VW is fitted with an approved wiring kit, professionally fitted which goes well beyond the old split charger relay. In fact the engineer changed a number of ECU settings with his laptop per VW and Westphalia guidelines. Never had a problem as described . I have auto switch off/on which is always active.
The latest Smart Combi relays fitted to my VW are switched on and off by an internal voltage-sensing system that senses when the vehicle's alternator is charging the vehicle battery.
I am told by my Tow bar expert mine is totally fail safe. Simply , no matter what happens with engine off , over run etc, the caravan battery cannot connect and drain via the car.
Seems to me the situation described is the fault of
a poor installation,
incorrect or failed Smart relays
failure to correctly re set the main car ECU per the manufacturer’s guide.