Defining Legalities in Divorce Decree

OK here is the situation. My divorce decree agreement is that we have joint legal custody and that I and my X spouse are to split medical costs after insurance has paid its portion. Simple enough!!!
Now add to the equasion that the children have had braces. The insurance coverage pays for most of the extras such as retainers etc etc. The heart of the matter is that the X spouse made a decision (without discussing the issue with me) to have an oral surgeon to do cosmetic surgery and do implants for the children. This proceedure is considered as cosmetic and thus insurance will not cover. The cost is to be about 15,000 dollars. Thus the X spouse is saying that I am REQUIRED to pay half. Now keep in mind that we split costs of MEDICAL not cosmetic proceedures. The orthodontist has verbally said that implants are not a medical necessity at this point in the childrens jaw structure development.
The big question is. Will I be help liable for 1/2 an expensive proceedure that is not deemend as medical.
In joint legal custody, both parties are to work together and agree on issues such as. Should one parents decision overide the others. Please advise.

That is an interesting situation. This will really come down to the wording in the order/agreement.