Just add a new bone in the middle of the torso of your character. The torso shape is currently partially bound to head bone and to femur bones so that's the reason it gets deformed when you offset or manipulate your puppet. Once you add the spine bone the torso should be only parented to that bone. If you don't achieve the effect just separate the bones (using the position tool) and the shapes (using the translate points tool) a little far away. It should work.