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Hello, is this happening on shore power or when the AC is running on the motor homes generator.
So far it sounds like a voltage regulation issue from the generator if this is happening on generator power, or a weak run capacitor if the AC is running on RV park (shore) power.
The fan running all the time should not be related, look for a FAN switch on the thermostat and set it to 'auto'.. if your thermostat has that feature.