If she files a tax return claiming the personal exemption of the child and the IRS accepts the tax return, then you will be unable to e-file your tax return. You will have to print and mail your tax return claiming the personal exemption of the child. If you are due a tax refund the IRS will pay you the refund.
Within a year the IRS will investigate why there were two tax returns filed with the same personal exemption being claimed on each tax return. You will need to respond to each IRS notice you receive since they will be asking for proof that you were entitled to claim the child's exemption. The loser of the investigation will have to pay back any tax refund along with penalties and interest.
See this IRS website for Form 886-H-DEP Supporting Documents for Dependency Exemptions - https://www.eitc.irs.gov/eitc/files/downloads/f886-h-dep.pdf
