When in the sitting position, always try and sit with your shoulders directly vertically aligned above your hips (i.e. not twisting) otherwise you will see a big movement left to right in the cross-hair.
If necessary, move your shooting cushion slightly and adjust your position until you feel comfortable otherwise unknowingly the muscles in your back will keep pulling you from side to side, hence the left/right movement you see in the scope.
Practice sitting correctly and you will hit more targets for sure!
(Same applies for standing shots).
Good luck, keep practising and you will see your score increase.