Can we sue ex for nonpayment of agreed bills?

Your wife can take him to small claims court. That might get his attention.

If I understand your question correctly and the facts upon which the question is based, your wife is the ex-wife of a man who has a court ordered obligation to pay a portion of the couple's children's medical and healthcare bills, but the man refuses to pay. If I understand your situation correctly, then the likely best option for your wife (not for you, unless you get standing in the divorce action between your wife and her ex-husband, which is unlikely and also most certainly not necessary) is for your wife to file a motion for order to show cause against her ex-husband compelling him to come the court and show to the court why he should not be held in contempt for failing to comply with the court's order to reimburse your ex-wife for the expenses she is incurred for the parties' children. I know you mentioned that your wife has been the court in the past and that the court has ordered the ex-husband to pay his portion of these medical bills, but that you still not paid and the court has done nothing to compel him to pay. Your wife needs an attorney who understands what kind of sanctions can be sought against someone who is in contempt of court. Particularly, your wife needs to know what kind of sanctions would be so severe that the ex-husband would prefer to pay for then suffer sanctions. One of those sanctions is jail. Your wife can ask the court to put her ex-husband in jail if he refuses to pay. Another thing your wife may wish to consider is working with the state and federal government and the court to obtain a writ that allows for to intercept her ex-husband's tax refund(s) to compensate her for the reimbursement euros but has refused to pay to this point. There are other options for collecting past due child support and medical bills, but they should get her started.

You cannot sue, as you are not a party to the terms of the divorce orders, and the children's bills are not your bills even though they are insured through you (unless you signed something at the doctor's office agreeing to pay). Your only option is for your wife to bring her ex up on contempt charges for failing to pay. This requires proof that each bill was provided to him in a timely manner. If he is held in contempt, not only can the outstanding amount due be reduced to judgment for collection purposes (the same as you would get if you could sue him, as the court cannot actually give you money, it can only give you a judgment) but she can also get sanctions, attorney's fees, and jail time in extreme circumstances.