Antifreeze coming in the passenger's side floorboard near glove compartment. The car might need a new heater core or a hose replaced.
Your presumption sounds exactly right to me. The only time that coolant enters the passenger compartment is through the heater core. If you have coolant leaking into your interior it is under no uncertainty that your heater core is leaking. I would recommend getting this replaced as soon as possible to prevent any future engine damage as well as to get your heater functioning properly for the winter months.
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