There are no "alerts" on social security numbers. If you try to claim a dependent and someone else has already claimed that person, the IRS computers will catch the conflict. Since you filed second, your e-file will be rejected. You
would then need to file a return on paper, claiming the child as
appropriate. The IRS will process your return and send you your refund,
in the normal time. Shortly (up to a year) thereafter, you'll receive
a letter from the IRS, stating that your child was claimed on another return.
It will tell you that if you made a mistake to file an amended return and if
you didn't make a mistake to do nothing. The other party will get the same
letter you did. If one of you doesn't file an amended return, unclaiming the
child, the next letter, from the IRS, will require you to provide proof.
But, since the child ONLY lived with you for three months; it's more likely that someone else can claim her. A qualifying child must live with the taxpayer for more than half the year. If the child lived with no taxpayer that long, the relative that provided the most support would get to claim the dependent. But the half year rule would disqualify them from the Child Tax Credit, the Earned Income credit, the day care credit and Head of household filing status.
