I would think that the first thing to consider would be the amp draw of the 4 ton compressor. Once you install the compressor along with an appropriate sized capacitor, are the existing wiring and controls going to be able to support it?
Is the breaker large enough to handle the amp load? Is the wiring large enough? Is the contactor large enough?
Even if all of the electrical is upgraded to support the larger compressor, is there any way that the coils are going to be able to handle the capacity of refrigerant being pushed into them by that compressor? A metering device can only do so much and I am picturing that little Dutch boy holding back the massive amount of water behind the dyke with his finger.
Is the indoor coil downstream from the electric heaters? Are the electric heaters allowed to operate at the same time as the heat pump does?
All in all I would have to agree with your dad.