Can my ex really claim daughter on her tax return?

When filing my tax return this year, my tax preparer told me that my daughter had already been claimed by someone else (presumably my ex-wife...her mother). In our original court decree, I was given the right to claim my daughter every year. I am the non-custodial parent and have never missed a child support payment. Now, instead of filing electronically, my tax preparer had me file a paper return and attach a copy of the divorce decree. Who will win? Will it take a long time before I receive my refund? Does anyone know if I need to fill out additional forms with IRS? Do I have any recourse against my ex for knowingly claiming someone she was not entitled to? I