Let me clarify things:
If you are ELIGIBLE to claim her daughter, she MUST say she CAN be claimed as a dependent.
If she CAN be claimed as a dependent (even if she is not actually claimed), she does NOT qualify for the Recovery Rebate Credit and her Standard Deduction is still based on being a dependent. So in MOST cases, you SHOULD claim your daughter as a dependent if you are eligible to claim her. She would not benefit if you do not claim her.
The purpose of that second box is for the American Opportunity Credit. If your income is too high to qualify for the credit, you would not be able to claim it. However, if you did not actually claim her as a dependent, she would have an opportunity to claim it on her return. However, she only qualify for the NON-refundable portion of the credit, so very often the benefit would be minimal or non-existent.
So for emphasis: If you are eligible to claim her as a dependent, she does NOT qualify for the Recovery Rebate Credit and is still subject to using the dependent Standard Deduction. So in most cases, you SHOULD claim her.
