The OP did not indicate there was a court order granting him the right not to pay if he didn't agree with the treatment. Further, if he didn't agree with the treatment, why wait 2 yrs before protesting? It sounds to me that the OP is more concerned about how long he has to pay the bill (2 months), rather than the bill itself. This would be dictacted by the decree, or what their local courts would consider reasonable. When I had to fight for med/dental reimbursement, my attorney said 30-60 days was considered reasonable in our courts.
The child had the braces put on in early 2004, so if dad had seen the child, he could have certainly inquired about what his half of the orthodontia would be, and start setting aside money or working with the orthodontist directly to pay his half.
"If she has already paid for them, then let her take you to court, it will cost her more in court fees and attorney fees alone just to get you to court, and even then she may still lose if it isn't your custody papers"
However, if the OP loses, he may have to reimburse mom for the dentist AND her attorney fees to collect them!