You daughter can not claim qualified education expenses that were paid with tax-free scholarships or fellowships, federal Pell grants, tuition grants from an employer, refunds from the school, and other non-taxable assistance to compute the American Opportunity Credit. The form 1099-Q is generally considered a non-taxable event.
The IRS is clear that the American Opportunity Credit can be claimed in the same year the beneficiary takes a tax-free distribution from a Qualified Tuition Program (QTP), as long as the same expenses aren't used for both benefits. The key words are "same expenses." Therefore, if the QTP only paid her tuition but not other qualified expenses (e.g. course related books and supplies), then minus the tuition, she can claim the other expenses to compute the American Opportunity Credit.
Your daughter (as a beneficiary) will still have to report the excess contributions by doing the following in her return even if the Form 1099-Q is in your name:
1. Select the Personal Income or Wages and Income tab
2. Click the "I'll choose what I work on" button
3. Scroll down to Less Common Income
4. Click Start next to Miscellaneous Income, 1099-A, 1099-C
5. Scroll down to Other reportable income and click Start
6. Click the Yes button on the “Any Other Taxable Income?” screen
7. Under the “Other Taxable Income” screen, type "Excess 1099-Q Dist"
8. Click Continue
