What you are expeiencing is the effect of Ackerman. Akerman is sometimes called "toe change in turns".
When you turn the steering wheel, the front tires don't turn at the same angle. Assuming the tires didn't slip, the innermost tire would need to be at a sharper angle than the outermost tire and the amount could be defined for every given steering input.
However, since tires need to develop a slip angle in order to generate the side forces to turn the mass of the vehicle, there isn't a specific steering geometry that can account for all of the possible combinations of steering input and speed. The best you can hope for is a good compromise.
So guess where the compromise is the worst? Right! At extreme steering inputs, which is what we do when we park.
I would, however, be absolutely sure the alignment is correct. If the toe is even a bit off the nominal value, you can get this.
Hope this helps.
