That issue is a classic case of the ac system being low on freon, your low pressure switch on the drier is causing that, its working as it was design too, its doing this to save you a compressor burning up. Put freon and it should be fine.
A cycling compressor can also be caused bt a blocked orfice tube causing the evap and accumulator to starve for refrigerant.On late model systems an overcharge can cause the same problem. An accurate diagnosis can be made with a set (high and low pressure) gages.