Re the van, from the factory the fridge 12v is always wired to the trailer plug; and never the van battery. Re the car, from factory,or an autoelec generally your car trailer plug wont have a fridge wire unless you have specifically asked for it. The fridge will drawer a reasonable amount of power, so as mentioned above the wire needs to be large enough to cope with the current and maintain an appropriate voltage (small wire and distance will result in significant voltage drop to the point the fridge wont be able to function)
From -1 to 10 in 4 hours, would suggest the 12v isnt functioning, which would be the case if you havent had your car plug wired to power the fridge.
Everyone modifies their vans, some significantly. Some clever folk do awesome mods using common sense and skill, unfortunately some clueless folk do all sorts of weird and stupid stuff. A look around the van should give you some indication if the list of previous owners may have been "modification nutbags", and whether any obvious mods would suggests they are the skill variety or the clueless clowns which may suggest they could have felt compelled to buggered with the wiring. It would be best to check it if your confiident, or have someone take a quick look over it.