How can I prevent the fireplace smell when the A/C is on?
One way would be a Heat Recovery Ventilator(HRV) that exchanges interior air for outside, which will relieve negative pressure.

Another would be a dampered (and screened) make-up air that connects to the cold air return (a low tech (and low cost) HRV).  These can be tied to exhaust fans or automatic via pressure differential.  You would want a HVAC firm to discuss options.

A third would be a cable operated chimney cap damper.  The stove may complicate this option.  I had one on a naturally aspirated fireplace and was good during rain and windy conditions that used to produce that "old fire" smell.