Keep house battery out of alternator loop for testing
What is engine battery voltage with engine running?
Perhaps your alternator's Voltage Regulator is only allowing 13.2v.
Perhaps it fried a diode or 2 and is only working on 1/3 or 2/3rd capacity.
Can't one check for AC voltage to determine a failed alternator diode?
If the Alternators voltage regulator is allowing more voltage than either battery, there will be no backfeeding going on when driving regardless of resting voltage differences between engine and house battery.
Thanks for bringing the cooler weather to florida, even Temporarily.