I'm assuming it's an Electrolux Dometic 3way.
Dont be concerned, this behaviour is completely normal. They work quite well on gas, OK on 240v, but 12v will only just maintain whatever temp is inside, for a short time. The 12v draw is around 10 amp, so don't leave it running too long on 12v.
When we travel, we usually have a 40l Engel running as a freezer, with the fridge for consumables. I've actually had better results by freezing about 6 soft gel type freezer blocks and sticking them into the Cub's 3way when driving, and not bothering with the 12v.
Just my experience, may not apply to everyone as it can depend on how well the fridge is vented, and if it a T or S model Dometic.
Cheers,
Spada