Does a non-custodial mother have any rights as to whether her 15-year-old son has seemingly unnessary surgery on both knees?

Your answer depends on the settlement agreement. It is typical to include language that the non-custodial parent has to be notified of medical procedures. You need to meet with an attorney and have them review the settlement agreement to determine your rights.  The information provided is illustrative in nature and not intended to be legal advice. Only with a full understanding of all the facts can appropriate legal advice be given. You are strongly encouraged to schedule a consultation with an attorney to fully discuss your matter.