My wifes 2012 XJL is currently experiencing a slight vibration through the steering wheel at low speed while turning left and right (about 3/4er turn at speeds about 5 MPH). I just picked up the car from the shop today (another $6k ticket) after having them look it over they had suggested a PS flush filter/reservoir replacement and identified all lower control arms, passenger side strut, rear lower A arm, sway bar links, and a few other parts needed replacing and the issue still remains. Now the issue is much less noticeable but it's still there! Has anyone else experienced this issues with their XJL and if so what was the fix?

 

The pulses will be from the PS pump, and it could be the serpentine belt that drives it is slipping slightly at low revs/speeds, so maybe check this out. What miles on the car as your shop seem to be indicating a fair bit of work needed on the suspension.

 

The car has 48k miles on it. I was thinking PS pump also but the feeling is not there when the car is stationary.

 

You'll only get pulsing when the PS pump is generating pressure and engine revs are low, at higher revs any pulsing disappears and when cruising little pressure is generated. It is a syndrome only at parking speeds.. When the car is stationary the fluid just circulates around at low pressure as there is no demand for "power".