You cannot find out who claimed your child on their tax return and the IRS will not tell you.
If your e-filed tax return is rejected due to someone else claiming your child as a dependent on their tax return then you will have to print and mail the return claiming your child, it cannot be e-filed. If your tax return has a federal tax refund the IRS will pay the refund.
See this TurboTax support FAQ for how to print a tax return for mailing when using the online editions - https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online...
Within a year the IRS will investigate this issue and the losing party will have to pay back any refund based on the dependent plus penalties and interest.
