The problem is not the pump, its the steering gear. The gear has a valve that controls the flow of power steering fluid for assist. There are two valves, on for left and one for right. If one of the valves is sticking, then you will have this issue. You can try and flush the power steering fluid with a cleaner for power steering or transmissions, but most likely it will not help. You are more then likely going to have to replace the steering gear.
The power steering pump only puts out pressure, does not respond different from one direction or the other.