I have hard water in my area and it causes mineral buildup to my plumbing. I'm replacing a leaky faucet with a new filter but unable to unscrew the filter from the sink because of the mineral buildup, that is in effect searing the filter to the fitting below the sink. When I attempt to unscrew with a wrench it will moves the fittings and hose below it and not separate the filter from its fitting. I've sprayed with liquid wrench and tried to hold down the fittings below the sink that's connected to the filter but with no success since it's a pedestal sink and access is restricted.

You keep saying "filter". Do you mean " faucet"? Remove the predestal for better access.