I'm no caravan expert, but it sounds like the 240v transformer bit has died.
I'm restoring an old Lunar Dino, 1981 vintage, and it has a line to charge from the car, when towing, but I don't use it at present. I don't want to mess around with possibly burning out my cars altenator, charging two batteries.
My van was not fitted with a transformer, so I've bought a simple, compact 240v to 12v car battery charger, which seems to be keeping up my 90amp battery, which is running my fridge water pump, and interior lights.
The 240v system has a consumer box with trip switches, which I've connected the charger directly to. So if anything goes wrong, it will trip and cut the charger off.
I'm going to buy a charge indicator, so I can see how the battery is doing without looking in the box where the battery and charger are.
Unless I have mis-read your post, you are running your fridge from the caravan 12v battery. On 12v DC, the fridge takes about 8 amps from the battery which will render the battery all but useless in approximately 4.5 hrs. Yes, I know 90 divided by 8 is approximately 10 hrs but the battery will be, to all intents and purposes, dead after approximately half that time. Not a happy situation!
If you are running it from the car while travelling, you will need to put a relay in the supply line from the car so that the fridge is only being supplied with 12v DC from the car while the engine is running otherwise it will kill the car battery and you may not be able to start the car. Taking 8 amps from your car alternator should not be a problem if you are travelling during daylight hours, i.e., no lights. If travelling at night, the car battery/alternator set up will have to cope with a requirement of approximately 15 amps for all the road lights plus another 10 amps if the headlights have separate bulbs at 60 watts rating (x2) making an intermittent load of 25 amps plus the fridge at 8 amps. This should not be a problem on a modern car although nowadays it is not unusual for the steering pump to be run off the battery rather that the engine so there would be an intermittent load there as well. Running the fridge on gas while travelling is a big no-no.
So much of the power system has been messed around with, I have no idea what it should be like. I'm learning as I go, based on my life's experiance fixing broken scrap.
In the manual I have from Lunar, it shows the power coupling between car and caravan, and which wires charge the van battery. I know which ones these are in the vans juction box, but they are not connected to anything.
All I have, as I've said before, is a simple 90amp battery connected to a small 12v charger, which charges at 2amps. I've had the caravan only parked in my drive hitched up to 240v, but I've had the fridge and lights working on test for a couple of hours, off the battery alone, and they seem to work fine.
I'll be only driving from Fleet to Wareham, about 2 hours, so I was happy with my test. The site we are going to has 240v hook-ups, so at that point we will be on 240v again, and the battery will be charging all the time off 240v. The fridge will be running off 240v, and that leaves a water pump and lights, which I'm sure the battery will handle. Gas will be for cooking and heating only.
I think I have all the bases covered, and what I have put together will work fine for the 10 days of our stay. Please remember I'm just trying to get something working for the least possible cost, for a once a year holiday.