Given the history and steerring input needed I would think it's not the tires. I've driven cars that move around (I call it wallowing) but you shouldn't have to go crazy driving it to keep it going straight even if the sidewalls move around a little.

Well, art is art, isn't it? Still, on the other hand, water is water! And east is east and west is west and if you take cranberries and stew them like applesauce they taste much more like prunes than rhubarb does. Now, uh... Now you tell me what you know.