can the student still choose to split the scholarship between qualified and non-qualified expenses as described above, even if she will be claimed by me?
Yes. But the student (not you) will pay income tax on the entire $13K not used for qualified expenses.
And does this allow ME to claim the $2,500 credit?
Yes, provided you have the tax liability to claim it against. Remember, a "CREDIT" is a dollar for dollar reduction of your tax liaibility. Whereas a "DEDUCTION" is a reduction in the amount of income you are taxed on.
So if before you take the credit your tax liability is for example, $1500, then the maximum credit you can get is $1400.
Now there's two portions to the AOTC credit. The refundable part, and the non-refundable part. I quite honestly don't recall the difference and how it all works. But I think @Anonymous_ does, or can flag another who does know.
I knew all the fine details on that when my own kids were in college. But it's been so long now that I forget that "fine detail".
