Options to Fix Nasal Flare when Smiling?

If your nose is normal in repose then there is no issue.  It may be that your smile does cause an over excessive flare but for you this is normal, as it is for many others.
As I agree with others botox can help with this but not significantly.

Botox can be injected but seek the care of an experienced injector. In some cases this may cause a lowering of the upper lip. If you find this undesireable, then the good news is that the result is temporary.
On rare occasion, I have performed modified alar weir excisions with a permanent alar cinching suture to hold the nostrils in place when animating. I have performed the alar cinching suture alone but have not been impressed with the results.

Nasal flaring can increase the apparent width of the base of the nose especially during smiling. It can be significantly improved by removing small wedge like areas in the junction of the nose and the cheek caller Weir or Alar resections.
http://janjuafacialsurgery.com/photos/prhinoplasty3.htm
Regards

 NO SURGERY!  The best option is botox which is reversible if you don't like it. Surgery can result in a permanent unnatural smile which can't be corrected.

The rhinoplasty is a static operation done for a static nose. On repose the nose will still widen, although usually it lifts after the surgery. Botox would be an alternative to try in this area. You do not want to have the smile muscle cut, it could look like paralysis from a stroke and would be permanent. Make sure that you do not need a Weir’s alarplasty in attempt to address the alar flare on repose.