I can't quite grasp why you would think that the Earth's rotation would change dramatically due to a change in magnetic polarity. Regardless, the answer is no, the sun will not begin rising in the west and setting in the east.
The Earth turning about its axis (not an actual feature like an axle) is going in one direction. When the magnetic poles switch as a result of the behavior of its molten core there won't be any appreciable change to the rotation of the Earth.
Perhaps a compass will point in the wrong direction, but the Arctic and Antarctic will still be in the same geographic location and still spinning in the same direction they were to start with.
Nothing to worry about.
