The tax preparer told you? Well, that's a huge no-no. But that aside...
it is possible that the IRS will cross-match the SS# and see that the dependent was claimed twice. From your facts it appears that you are entitled to claim your child but there is a risk that you will be asked about it since you filed second. I think the best you can do is truthfully and fully file your return and provide proof later if asked. Make sure you have documentation to support the filing and discuss it with you tax preparer who may not be the best if they are disclosing private information!
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
Claiming your daughter as a dependent won't necessarily trigger an audit of either return, but the IRS will discover that two different parents claimed the same child, and someone's exemption will be disallowed. If you have proof that you're entitled to the exemption over your ex-spouse, then you will most likely be given the exemption - but it will probably take a while to be sorted out by the IRS. In the meantime, you won't receive your refund check. Do you have a marital settlement agreement or final judgement that addresses which parent will take the tax exemption?