It doesn't matter which one of your paid her tuition.
The person that can claim the tuition credit is the person who claims the student's "exemption". If you daughter claims herself on her tax return, she can claim the tuition credit. If you claim her as a dependent, you claim the tuition credit.
Furthermore,
There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working. You (she) cannot be supporting yourself on parental support, 529 plans or student loans & grants. You must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit. You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
There is somersetting else you both need to be aware of: starting in 2018, a student, with earned income, usually gets the same amount of refund (or pays the same amount of tax) regardless of whether her parent claims her as a dependent. or not.
