Can I be forced into paying for braces that I cannot afford at this time?

Well your child needing braces is not really optional, the Dentist does not just request braces,there is a reason. If the court order stipulates you have to pay half of medical bills,this would be included,having joint custody may allow you both to make decitions for the child,it does not mean if there is a medical condition,that you can just say no,and feel fine with it, that is why we have the courts,if you and the father cannot agree,and there is a stipulaton you are to pay half,he can file a motion asking the court to make you pay,or he can pay his half and take you to small claims court and get a judgement against you, what you might want to do is see if you can make payments to the Dentist for your half,that usally can be done with braces.

The braces are for cosmetic purposes only and are not a medical necessity

I understand what your saying in one way and in another, as a mother I would want my child to have this done,while young, it not only helps her teeth,but her appearance, if the father can afford to do this and the child will benifit from it why wait, maybe the father will cover the whole thing,if you cannot,if he feels this strongly about it, after all if you do not have he money than you don't have the money, if he takes you to court,let he judge determine if he/she feels this is medical necassary at this time.