I have a Carrier thermostat like yours, but I never turn on the dehumidify control. This control will overcool your house to about 3 degrees below the temperature setting, which will make the house too cold. I have never had an issue with high humidity. I have no idea what the Honeywell device is controlling. Hopefully, it is not adding moisture to your house which will work against the dehumidify setting on the Carrier thermostat.
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