The BS7671:2008 known as 17th Edition wiring regulations decided for some reason to include the 12 volt wiring to a caravan, one of the things they stated was the supply to charge the battery and the supply to work the fridge need to be independent, however the caravan only has two supplies one permanent when ever the caravan is connected to car, and one only when the ignition is switched on, and both battery charging and fridge only want a supply when the ignition is switched on, so only way is to use a relay, so the non ignition supply is switched on when the ignition supply is made live.
This means you need both supplies, even when you don't need anything to work with the ignition off.
The ignition switch is not normally man enough to take the power to the caravan and what is important is when the start button is pressed, that the caravan battery can't supply power to the car, as the current from caravan to car is far too high, there is also the problem if left plugged in the caravan could discharge the car battery, but compared with the start current problem that is minimal.
So early in the caravan usage we got the blocking diode, this seems good, but the diode reduces the voltage by 0.6 volt, with the old CAV 440 regulator this was OK as you just moved the spade connector from Med to Hi and lifted the alternator output to suit, but that may have been OK with wagons, but cars did not have an adjustment on the alternator regulator. So the blocking diode lost favour, the next was the relay, by powering the relay from the warning light output from the alternator, it insured contacts open until after engine started.
However may French cars used single phase alternators and the system would not work with them. So came the voltage dependent relay, it only switched on at 13.8 volt and off at 12.8 volt so it would ensure caravan battery not connected.
Then came the schottky diode, unlike the old blocking diode these don't have a 0.6 volt drop across them, so worked far better, however not cheap,
Sterling power version £40.80 and although not 0.6 volt there is a small amount of volt drop, however with the use of a battery to battery inverter they are not required.
So with a battery to battery inverter the power can't flow caravan to car, it can flatten the car battery if left running, but it does two things, one is it charges the caravan battery faster and two it stops the back power caravan to car, and the best location is in the caravan.
So now we have a problem, there is no standard way to wire, if you have a simple relay connected to ignition supply that will stop the caravan being supplied when ignition is off, so it will stop the car battery discharging, but not all cars turn off the ignition when cranking, and if it does not turn off the ignition then it could burn out wiring between car and caravan, so the only way with many cars is to fit the schottky diode as that is only sure way to stop supplying car from caravan.
I know the subject is fridge, but it is not the fridge which is the problem, it is charging the caravan battery which is real problem, personally I have disabled the charging of caravan battery from the car, with a tow time of maximum 4 hours, between sites, going home does not matter, and going from home does not matter as former battery can be charged once home, and latter battery fully charged anyway. So 4 hours between sites, and with a split charging relay it may start at 30 amp, but within a mile down to less than 5 amp, so that 4 hours is likely just 10 Ah into the battery, hardly worth bothering about, so it is either a battery to battery charging inverter which means you may get 30 Ah in 4 hours, or solar panels, and if you are living off grid the solar panel seems the way to go.
But this means some discussion with the tow bar installer as to what he is going to do, simply I want caravan electrics fitted is not enough, you need to say what you want, the two bar fitter can guess, and he has three options 1) schottky diode. 2) voltage dependent relay. 3) simple fuse and ignition relays. With the latter should the engine be cranked with the caravan battery connected it will simply rupture the fuse.
There is nothing oddly in BS7671:2008 (yes I know now 2018 but I don't have a copy of that) to say about the problem of reverse power caravan to car, and some cars pressing the starter does switch off ignition power, but to be fair all the tow bar fitter can do is fit the manufacturers wiring loom and follow their instructions, and many German cars the loom does not support the two supplies to the caravan.
The most important thing is where there is an electric anti snake device that the battery charging does not cause the supply to this from being interrupted.
But you can't blame the electrician who wired the car, unless the caravan was there with the car when he wired it, He has not got a crystal ball, he does not know how your caravan is wired.
Personally I see no future in split charging, my wife's car has the charging controlled by the engine management, and I have during the lock down needed to use a smart charger to recharge the battery as car not used enough, it can't even keep its own battery charged never mind one on the caravan.