Another Update:

The shop replaced the pump and the steering gear box with new factory tie rods and everything. The horrible vibration is gone, BUT there are still some shuddering when I turn the wheel relatively quickly with the car just sitting there with tires on the ground. It will also shudders when I do slow speed left or right turns with relatively quick steering inputs. Therefore, it's basically back to where I was BEFORE I started messing with the pump and before that horrible vibration happened. Only now it's worse because it didn't use to happen when the car is just standing or when I do right turns. It only happened when I did left turns previously.

so this is NOT over. I ask them to spend another day to look at other things like suspension or whatever, but I think they are also stumped at this point. They replaced everything in the steering system other than the lines. Could the hoses/lines be causing that? or Could it just be some left over air in the system that may magically go away after a few days?

Any other ideas? I am feeling more and more hopeless at this point.

 

Right now it could just be air in the system and not having enough constant pressure, perhaps?

 

have you fixed this?