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May not be the heater core at all ($$$ to fix I think due to being pretty laborious), but the the blend heater flaps control.

Quite a few topics on that.

 

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Sunroof tubes can be clogged.

Or maybe the AC condensation tube disconnected?

Soaked only when it rains?

 

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heater core failures are kinda rare I think.

How many miles on the rig? How often do you flush the rad? And did you use mopar-approved coolant if you have?

Possible windows are fogging up due to the condensation in the cabin from the soaked carpets.