Advised by an Orthodontist to Have my Upper Palate 'Split' (His Words) Open to Fix a Cross Bite on the R/h Side (photo)

Ideally, expansion is done prior to 8 years of age.As an adult it is more difficult.  The ALF and Damon Braces give a moderate ability to expand the maxilla.The SARPE Procedure allow Rapid Palatal Expansion by utilizing a Surgical Assist.  It is an excellent and rapid method of palatal expansion.  There can be surgical complications with the SARPE procedure.Epigenetic Orthodontics with the DNA Appliance is extremely effective but slower than SARPE expansion.  It is more resistant to relapse, has no surgical complications and is only worn 12-14 hours/day so is friendly to still having a life  without appliances during the dy.  The DNA Appliance will be one of the most cost effective methods to correct your issues.Ira L Shapira DDSDiplomate, American Board of Dental Sleep MedicineDiplomat, American Acdemy of Pain ManagementRegent & Fellow, International College of CranioMandibular OrthopedicsChair, American Alliance of TMD OrganizationsThinkBetterLife.com

You certainly do have a crossbite on the right hand side.  

I would strongly recommend fixing this issue orthodontically, rather than masking it with vaneers.  The underlying problem is the narrow upper jaw. Also, if you look, your smile line is what we call 'canted' - which means your teeth are higher up on one side versus the other (in your case, it's higher up on your right side).  This is also best corrected via orthodontic treatment rather than vaneers.  

The question of whether or not this requires surgical expansion or just orthodontic expansion will require a more detailed exam, of not just your teeth, but also the bone that surrounds it.  The reason why surgical expansion in adults is sometimes called for is that it prevents the teeth from being pushed and tipped too far towards your cheeks, so as to avoid recession (bone loss).  

I would get a couple of opinions from certified orthodontists so that you can be comfortable with the treatment that you choose.  What was recommended to you as far as the treatment option goes, is quite standard and not out of the norm.  

Expansion of the upper jaw does not require surgery.  Older traditional training taught dentists that the upper jaw bones fuse together by the teen years and that surgery is required for widening the upper jaw.  This actually was incorrect teaching and the widening of the upper jaw can be accomplished at any age.  The key is to find someone who understands this and will use slow palatal expansion (SPE) with a removable treatment appliance.  In our office we have done this for the last 28 year on thousands of patients, some into their 70s.  It is The New Orthodontics and has much fewer limitations of what can be done without surgery or removal of permanent teeth.  Keep looking for a dentist/orthodontist who understands this.