the steel belts would change the pattern & the steel belts would separate especially in the side walls.
I am not sure about all manufacturers, but none that I am aware of ever put steel belts in the sidewalls. Steel belts as far as I know are only under the tread.
As for belts running in the opposite direction if you move side to side..this is always the case. For example, when a white letter tire is made, the belts are running in a certain direction and the tire is cured with, for example, the white side up in the tire mold. This means all belts are running the same direction. When you put two of these tires on the drivers side and two of these tire on the passenger side, the belts are already running in opposite directions due to the white letters being outward. There is no danger in changing non-directional tires side to side.