Object B's position to Object A as a controller for object A's animation The best way to describe what I'm trying to do is the example of a mickey mouse head. Facing the head from the front the ears are full circle, both on the same height. When viewed from the side though they retain the full circle while one sets lower than the other. (the object B in this case would be the camera) 
I basically want to have certain movements to happen depending on where object B is in relation to it or its bones. Is this achievable in Blender?
If I correctly understood what you want, you could do it with a Track To constraint: Give your object A an armature, and give the bone that is supposed to move according to object B a Track To constraint, with the Camera as the Target. Now when your Camera moves, the bone will follow.