Many times this is caused by using too many, and generally not the right, muscles to draw the bow. Trying to consciously place the elbow at a given place is also counter productive. It sounds trite but try to relax the draw and only use muscles to move the upper arm and shoulder on the string side. BICEPS especially need to be relaxed and NOT used. IF!!! you do this, your string arm elbow will naturally be in the right place with no effort on your part.
Again, in general, if your hand pops out from your face at release, this indicates arm muscles and no back use. Allowing the hand to move forward on the face kills any back tension you may have established and is not good.
No "chicken and egg" more like trying to kill the golden goose to get more gold eggs.
Arne