No. It is not possible to "flag" an SS #. But, it is NOT true that you they have to collect from her for you to get a refund.
This is how it works: If someone else claimed your child (including a foster child that you had for more than half the year) inappropriately, and if they file first, your return will be rejected if e-filed. 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. Be sure to reply in a timely manner.
Winner gets the tax benefits; loser gets to pay the IRS back with penalties and interest.www.eitc.irs.gov/EITCCentral/f886-h-dep.pdf
You situation is better than most, as you have had them all year. But once a competing claim is filed, you'll need to prove it. It's the split year situations when biology may trump weak documentation