My dometic fridge will work fine when I plug it in the AC 110 Volt the night before a trip. Connecting it to the cigarette outlet (12 V DC) once driving it works fine: the back of the refrigerator dispels heat and the cooling system is ice cold. So far so good. Starting the fridge the next day by plugging it in again while driving into the 12 V socket nothing happens; later I find that the 10 Amp fuse in the cable from the battery to the socket was blown. Replaced it; it worked initially, then blown.
So it seems that the battery can supply the fridge with enough power to keep the temperature down IF THE UNIT HAS BEEN PRECOOLED WITH AC, but if it is challenged to start cooling a room temperature unit it draws to much power from the battery that the 10 Amp fuse blows. Any advice is welcome.