Re: Prone Shooting Question
It's kind of hard to say anything without seeing your shoot, or at least pictures of your position.
I'm not sure if you are saying the rifle stock is moving in your shoulder or the barrel is moving left to right or right to left.
BUT the rifle shouldn't move in your shoulder at all. A propper position would create a pocket for the stock to set in.
Get a sling, if property fitted, firm but not uncomfortalbe it should create a situation where the stock has to be "snapped" into the shoulder. Cocking your leg (shooting side) up helps lock the stock into your shoulder. This also shifts or rolls the body a bit taking the weight off your diaphram allowing for smoother breathing. The right or shooting lower leg should be lined up with the barrel of the rifle. This help to keep the natural point of aim under recoil.
The head should be as straight at possible while allowing the full weight of the head to rest on the stock giving your the "chipmunk" cheak. The left or none shooting elbow should rest directly under the stock. The stock rest on the non-shooting hand without undo pressure or grip. Elevation is obtained by slidding the hand under the stock.
Windage is obtained by shifting the hips (and body).
To test this, dry fire, get a natural point of aim, proper sight picture, then close the eyes and pull the trigger. Open your eyes and see if you are sill lined up and on target. If not adjust your postion and repeat the process.