My nose pulls down when I smile making it seem even bigger. What treatment would you recommend? (photos)

This is due to the depressor septi muscle as described by the previous surgeons. A surgical procedure resecting that muscle along with some resection of septal cartilage to shorten the nose and rotate the tip slightly may be needed. You also seem to have a dorsal hump on the limited view which you might want  to correct. You will need to consult with an experienced rhinoplasty surgeon to examine you in person and address your concerns and desires.

  The reason that the nose droops with animation and smiling is  because of the presence of a depressor septi ligament. To reduce and eliminate this tethering, surgical releasing of the depressor septi ligament is required  during a closed rhinoplasty procedure. To reduce the dorsal hump requires shaving down the cartilage and bone along with osteotomies. To lift the nasal tip requires a tip-plasty.  All this can be accomplished with a closed rhinoplasty approach with all the incisions placed on the inside of the nose itself.  For many examples, please see the link and the video below

The nasal tip is pulled down when you smile because a specific muscle, known as the depressor septi muscle, contracts to bring the tip closer to the lip. This can be very significant in some individuals, especially those who already have a ptotic (droopy) nasal tip. Permanent treatment is easily achieved by cutting the muscle attachments to your nasal septum, but certainly such an approach should ideally only be considered if you're contemplating making additional changes to the outside or inside of your nose. Fortunately, injecting botox to the muscle can paralyze it, resulting in a temporary improvement in the enlongation of your nose when you smile, lasting 3-4 months on average. A word of caution, injection of too high a dose of botox or too close to the lip can also cause the lip to drop change your smile, so your surgeon should understand the anatomy that he/she is treating. Best of luck :)!