Not sure how to advise you on the refring.
You should have a 120V panel with breakers; there should be a breaker for the AC. Shut it OFF. Sounds like you have some sort of relay that has welded its contacts together to keep the compressor running; that may be internal to the AC or external, I'm not familiar w/your rig. After that breaker is OFF there will be no 120V to the AC, but the rest of the breakers should still be live. You should be able to diagnose the refring after that w/out interference from the AC problem.
Baja-tested '08 2-slide 36'
Alpine: The Ultimate DIY'er Project