I find the biggest problem with GM traction control is with the yaw sensor and the steering angle sensor. When the yaw sensor goes the vehicle will lock up the brake of the freewheeling side when turning hard to the left or right . when the steering sensor goes the steering wheel shudders when doing long slow curves however you mentioned a strong hard shift or jerk between shifts . This sounds like the throttle actuator. But before you get to excited about changing anything check the transmission fluid level . If the level is overfilled ,or low ,it can cause the transmission to shift odd and this can cause the traction control to throw an error code. you may want to check that before letting them change anything. Hope this helps