It would be nice if you could do voltage measurements while the engine is running, the auto battery is charged up and the trailer battery has been run down a bit. The voltage difference is what will show how inefficient this is. The voltage at the trailer will drop even more when you run the fridge. It would be even better if you could find a clamp on DC ammeter to show just how many amps reach the trailer battery. Unfortunately, these are not easy to find. I made these tests a few years ago for some friends, just to show that it doesn't really work, but I do not have exact numbers I can post.
Full time boondocker, solar powered, no generator