This kind of problem has been reported on the forum in the past and usually it means that the factory (or previous owner) has plumbed the cold city water input line into a Hot line somewhere in the coach. That would give you cold on the Hot side of faucets when on city......the strange one is getting Hot from the cold side on faucets.....so city water flowing backwards through the hot water tank possibly? Usually there is a check valve on the hot water tank outlet to prevent reverse flow (not sure if that is universal or not though) so maybe not equipped or check valve possibly failed on your ACE.
You will need to try to trace out the city water pex line and find out where the wrong connection has been made. Don't know your ACE configuration but it would be ugly to trace on mine. Try removing lowest drawers or access panels where possible until you can find where they tied into a hot line instead of cold line. Then potentially more fun trying to correct it. Pex crimpers might be a challenge depending on space available......shark bite fittings to fix this might be useful.
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