Your 2 12v batteries could probably run the inverter for short periods. Do you know what size wire is used to connect the inverter to the batteries?
I don't have your RV or an 1800W inverter. From your post I gather they didn't wire the inverter to the items you mentioned. Probably didn't because of the high current drains.
If they are wired and the inverter just can't handle the drain, its probably because you need larger wire or more batteries, or both.
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