What you need to do is install something that prevents the battery in the caravan "back-feeding" into the cars electrical systems. When the alternator is running and the car's electrical system is running at circa 14.1v - 14.3v then current will always flow into the leisure battery - i.e. charge it. But when you turn the engine off, depending on how the live connections are wired in the socket, there is the potential of the leisure battery supplying power to things on the car - this is not a good idea. The other problem is the caravan can also draw power from the car - meaning that car battery could be flat when you go to start it.
This can be done easily with a simple relay, which only connects the caravan battery into the car live system when the engine is running and the voltage is high enough to charge it, see this:
https://www.vanlifeadventure.com/cam...harging-guide/
You should also check if your car is fitted with one already. If the pins are only live when the engine is running (opposed to just the ignition being on) then there probably is such a device.