I was talking to someone who went to a hunting/tracking camp type thing. He said, the instructor told them that deer have dominant sides like humans have dominant hands....so if the deers right side is dominant (you can tell by looking at tracks of the animal) then that specific deer takes longer strides with their right half resulting in a leftward running circle.

IDK if this even relates to what you're saying, but I thought it was interesting...I guess then if the does is chased long enough, she should form the circle, right? ...but I'm guessing it's more random jumping out of the way of bushes while on the run than any other factor that determines circling.