Why do the corners of my mouth turn down when I smile? (photo)

The movement of the corners of the mouth is secondary to the activity of the facial expression muscles. However, the anatomy of the face ( bones, soft tissue etc) could affect the movement of those muscles. Also aging affects the corners of the mouth . In aging patients treatment of the muscles that lower the corners of the mouth with Botox help to turn the courses of the mouth up at rest and when smiling. 

I would recommend Botox in your DAO muscles. This requires 10 units of Botox, total. You can actually see a dimple below the corner of your mouth which I suspect is the action of the DAO pulling on the corner of your mouth and skin. Best.