As @xmasbaby0 stated, the rejection notice should indicate which dependent was claimed on another return by number - i.e. the numerical order that dependent appears on your return. The first dependent is labeled 01, etc.
If you are certain that you are the one who qualifies to claim both dependents, the other parent won't tell you whether they claimed them, and your dependents didn't file and claim themselves, you can file your return by mail. The IRS will select both returns for examination and ask for information to establish which taxpayer is entitled to claim the dependents.
After a return claiming a particular dependent is accepted, any subsequent return that is electronically filed claiming the dependent will be rejected by the IRS.
See this TurboTax article for more information on duplicated dependents and this one on how to remove a dependent.
Depending on your income and your tax liability, removing dependents may not make as much of a difference to your refund or balance due as you expected. You can preview your return before filing to find out how your taxes were calculated and to view the forms and schedules. See here for details.
@lcipolla
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