Based on what you have told us, I am concerned about the radio which you tell us is permanently connected to the caravan battery, and that you don't have the wiring to charge the caravan battery from the tow vehicle. These are both modifications to what would have been the factory standard wiring when the caravan was built in 2002. It begs the question and concern that there may be other non standard modifications, which we can not know if they have been carried out to a safe standard.
I was under the impression all new UK caravans built in 2002 could accommodate a lead acid type leisure battery of about 100Ah capacity in the standard battery box.
From the picture you have added to your opening post, it seems you have a fairy typical 230Vac to 12Vdc power supply/charger that uses a Switched Mode converter. These produce a regulated 13.8Vdc which will run the caravans internal 12V items when you have and recharge an LA battery on good condition safely. As you have a caravan mover, and if you want to use it, you must have a battery to provide the current the mover needs.
You tell us you need 12Vdc off grid capability for a week. This posses more of a challenge, and you will definitely need a good battery, and skills at being economic with your 12V usage. Energy saving tips such as changing all the lights to LEDs, making sure you turn everything off when your finished with them, be wary of the things that continually sip power over longer periods, like lights, modern TVs, are much better than older ones, but they can eat a surprising amount of battery charge.
You might consider getting a 100W solar panel which over most days (even cloudy ones) can make a usefull contribution to the battery charge and extend the off grid capability by a few days.
Be warned, if you are off grid, the battery may be down on charge by the end of your stay, and it might not have the energy to run the mover.