You do not pick and choose whether you claim your daughter as a dependent.
If she is under 24 and a full time student and you provide more than half of her support for the tax year, you can claim her as a dependent. If you do not claim her, then you lose the Other dependent credit of $500.
On her own tax return, she is asked the question whether she paid more than half of her own support. If the answer is No, then she has to say that she can claimed as a dependent by someone else. And she will not be eligible for the stimulus payments. As someone who can be claimed as a dependent but is not actually claimed, she can only claim the non-refundable part of the American Opportunity credit, but not the refundable part. As her income is less than $12,400, she has no tax liability and the non-refundable part of the AOTC does not give her any tax break.
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