We replaced our Dometic with a Norcold last year. The Dometic died - or I should say the price on a replacement part that may or may not have fixed it was ridiculously expensive. We got a 3 way so it could run on battery too, but I later found out it was not necessary. You will run your fridge on gas and AC. The power requirements and the limited cooling ability on DC simply don't make it worth it. When we are plugged in, which is rare, we run AC. When we are traveling, we run on gas all the time. In some places you may need to turn the gas valve on the tank off for a few minutes while you refuel, then open it again when you pull away from the pumps.
The DC wiring requirements for the Norcold to be connected to a TV are a huge hassle also. It requires heavy gage wire and a special circuit. Quite frankly, it was not worth hooking up. As for the wiring requirements of the Dometic, you should probably check them out to make sure that it's really worth hooking it up. When I was going though the replacement effort, I spoke to a guy who specializes in repair of RV appliances. He said the DC for refrigerators in trailers is a waste of money.