The other posters are right. Based on IRS rules she would have the right to claim exemptions, etc. because she is the custodial parent (according to IRS and court order -- IRS defines this slightly differently based on actual physical custody of child). People tend to think because they have a court order that says that they can claim a child that they can w/o regards to IRS rules. No court order is going to be an excuse for filing your taxes wrong. If you are unsure how to file, seek out a tax professional.
If you are the custodial parent (by IRS standards) you can within the rules:
1) claim the exemption
2) claim the EIC
3) claim the Childcare credit
4) claim the Child Tax Credit (and Additional Child Tax Credit as applicable)
If you are not, then you can claim the following but only with a signed Form 8332 by the custodial parent:
1) claim the exemption
2) claim the Child Tax Credit (and Additional Child Tax Credit as applicable)
Now keep in mind this a simplified version of the requirements but if you're unsure how to properly claim credits and exemptions after a divorce, seek professional tax advice.