Common ground on caravan for battery and towing vehicel

Hello everyone,

i want to have a batterie in my caravan.

At the moment there is only the power of the towing vehical on the input 
to the 12V "network".

I want to have also a battery. My plan is to switch of the battery when 
the caravan is pluged into the car. This should be done with a 40A 
relay.

My question is: is it nessesery to do it also with the ground wire, as 
in the attached drawing? Or does just one relay on the "powerline" just 
fit?

Is there a danger for the electronic in the car or the battery?

This is no advanced electronics question and i hope my english is good 
enough!

Hope to get help!