Hi Robert,
From the title of your posting I an not sure you appreciate the difference between the 12V coolers and fridge. - Please forgive me if I am wrong - but,
There is a significant difference between the 12V coolers and a portable refrigerator. I have both and they each have their uses and duties.
The 12V coolers use a peltier chip, and they have quite limited ability. They need an external mains adaptor to allow them to run on mains power. Typically they can only produce about 15 to 18C difference between the inside of the box and the external ambient. In many cases this might be enough for a pic-nic, where it can be powered in the car during the journey and the noise from the fan can be tolerated for the duration. At the pic-nic site it can be unplugged and used just as a cool box. It can be more easily carried having handles and it is inherently lighter than the fridge box.
If you are looking for better performance, and with more power options, then there are portable refrigerators that use the same system as your caravan fridge are available. As you might expect they tend to cost more, but you have the option of 12V dc, 230V ac or gas, and superior cooling abilities
Both the cooler and the 12V circuit on the fridge use quite a lot of current, and so it is unlikely you could use them for long on battery only. They are really designed to be used when the car engine is running.
I use my multi-fuel fridge box when not on holiday I also use it at home to keep the weekly shop of milk, fruit juices, and beer chilled and ready to use.