Shaking when turning or at high speeds

If there is a vibration there is a problem. I would be getting the tire and rim re checked for run out. Ensure that the wheel bearing is okay, there should be no sideways movement in the bearing at all and no roughness when spun, and steering and suspension components are sound and serviceable. If you hear or feel a noise there will be a problem. Also, check drive shafts for excessive noise and slop in the CV's.