Ok...let me clarify a few things.
If you have been faithfully paying your child support, and if you have a court order stating that this is your year to have the exemption, most likely the IRS will honor that.
What will happen is that whoever files first will be able to file electronically. Whoever files second will have to file a paper return, because the return will get rejected electronically.
Your returns will be processed normally (at least if the IRS follows the same proceedures that they have the last two years...there is no 100% guarantee that they will do that). Then later in the year you will both recieve a letter regarding the double claiming of the exemption and they will enourage the person who claimed incorrectly to amend their return.
If no one amends their return then they will start asking for proof. Here is where there is a slight chance that it could get tricky for you. You see, the state court judge really doesn't have the authority to make orders regarding the tax exemption, even though they do. The IRS regs actually rule on that issue. Therefore the IRS is free to rule in mom's favor if the IRS determines that you did not provide more than 50% of the child's support.
Like I said though, the IRS normally honors the state court orders, therefore they are unlikely to do that unless you have arrearages...you just need to be aware that it could happen.