Q: Vibration while stopped when engine under load (AC + full wheel lock); more noticeable w/ cold engine

My car has had vibrations when turning the wheel and the car is stopped or just start moving slowly, e.g., when I am pulling out of my garage in the morning. The whole car vibrates; it can be felt in the steering wheel, seat, and floor. It is definitely more noticeable when the engine is cold and under load, like when AT is in Drive, the AC is on, and steering at full lock (left or right). When the car warms up the vibration is still there but less noticeable. The car has been to the dealership for this problem twice but they say they could not reproduce the problem. The front and side motor mounts were replaced but that did not change anything. The rear motor mount has been inspected twice and is fine. Also, AT and PS fluids were changed. To me it seems like it's either a pulley or the belt tensioner issue but I have no way of diagnosing. Do you have any other suggestions on what to check? Thanks.

My car has 85000 miles.
My car has an automatic transmission.