Palate Expander Open Nasal Air Way?

Your ideas about how a palatal expander may help you are right on!  It can broaden your smile and improve your nasal airway.  Since Invisalign is not good a expanding the palate and widening the arch it would have been better if you'd had the expansion done before the Invisalign.  That way the Invisalign could adjust your teeth to fit  accurately in your new bite.  You might be able to consider asking your orthodontist if he/she can stop the Invisalign, expand the palate, and the take new impressions for a "mid-course correction" in Invisalign.  That way you might be abale to obtain the result you're look for without spending more on an entirely new case.

You are probably just in time to be treated w/a palatal expander.  They are less effective once your bones have fused and stopped growing and you're probably pretty close to that.  Make sure your dentist does it slowly and you may need some orthodontic fine tuning after you're done.  It will absolutely widen your smile and improve your air flow.  As Dr. Lauson said, it will not only improve your smile, it may improve your health and your quality of life!  I treat TMJ pain and migraine patients as well as sleep apnea patients and the great majority of them suffer from a narrow palate.

Congratulations!  You really do get it!  Most orthodontic patients have a narrower than ideal upper jaw (95% by a recent study)  This can not only lead to crowding and overbites, but later TMJ Dysfunction and even Obstructive Sleep Apnea, so the small upper jaw needs to be taken seriously.  Invisalign is limited in how much you can widen the upper jaw.  What you need is Slow Palatal Expansion with a removable treatment appliance which can cause a widening of the upper airway as well as give you that full beautiful smile.  Have a treatment plan that has you widen the jaws first, then Invisalign.  I have successfully treated hundreds of Invisalign cases this way.