What options are there so my nose doesn't move when smiling after rhinoplasty?

this problem is mainly a result of poor tip support - you would likely benefit from structural grafting of the columella and tip

In some patients, the attachment of the nasal muscles in the central portion of the nose can pull the nose down while smiling. The easiest way to correct that is to snip that muscle during a rhinoplasty procedure and place a graft to prevent it from reattaching and support the tip of the nose. I hope this information helps.

Nose droop on smiling is a common problem when the tip is ptotic and underprojected. It can also occur when there is "tension' in the nose because the nasal septum is pushing it down. rhinoplasty can correct this for you permanently.

This not an uncommon issue. Usually I cut the upper lip muscles slighly and most importantly, I support the tip with a cartilage intercrural graft. Cinching sutures have been used to narrow the nasal base but, often lead to asymetry and discomfort.

By the sounds of it, you have a plunging tip.  You had this addresses and want it back.  There are a number of surgical maneuvers which can be done to address this issue either by way of muscle cutting technique, implant or grafts.