Which is best for me, submentosplasty only, or submentoplasty + facelift? (Photo)

aka Platysmaplasty after the specific muscle addressed is not enough tot address your concerns. The Platysma needs to be tightened laterally via a facelift incision and the residual skin removed. I suspect from the term sidelaze you cite your doctor is talking about cellulaze. This imo will be inadequate to give you an acceptable result.

I see significant laxity of the lower face and neck. In addition, you experience volume loss due to decrease of facial fat tissues in certain areas. Therefore, I recommend for best outcome face and neck lift with facial fat grafting. 

You are correct in your assessment. Any procedure short of a facelift/necklift with submental repair will leave you disappointed. I am a firm believer in minimally invasive procedures when they will solve the problem but when used improperly nobody wins. Find someone who is willing to solve the problem.

I think a well executed full facelift will give you an excellent result. This takes care of everything from the lower eyelids to the clavicle. The downtime is the same as any miniaturized facelift.

Thank you for the pictures.  I am not familiar with the procedure you are considering.  My recommendation would be a full facelift/neck lift.  Please visit with board certified plastic surgeons for the most accurate recommendations.