So what I found out about Dometic refrigerators was when I broke the ground, the refrigerator would turn on but would not get cold.
We were at a trip and took off with the trailer still attached to shore power, like many, I leave it hooked up litterally until we pull out because you know people will be going in and out of the trailer all the way until the last minute.
I took off, breaking off the ground prong. After that, the Dometic refrigerator would not get cold. It would come on, but it didn't show a fault either, just stopped working.
I would use a 3 prong ground fault tester. I keep one of these in the RV now. Keep in mind, so much electrical safety is built into these RV's to stop onboard fires, this also makes is very sensitive to wire problems.
https://www.homedepot.com/p/Power-Ge...0542/206212329