"It appears that we would not be able to claim the AOTC ..... and then we would have to show the extra scholarship income that she received as income that is taxable on her return"?
That's generally correct; but there is a loop hole* available.
The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.
Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.
You essentially have to use a work around in TurboTax (TT). Here's how I would do it. Enter the 1098-T, on your return, but only enter $4000 in box 1. No other numbers. You only enter the 1098-T to get TurboTax to check the proper box on form 8863. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS.
Enter the 1098-T, exactly as received, on the student's return. In his interview, you should eventually reach a screen called "Amount used to calculate education deduction or credit" Be sure the amount in that box is $4000. That will put all his excess scholarship as income on his return.
Be advised some people are saying they're not getting the "Amount used to claim the tuition deduction or credit" screen on the dependent’s . The alternate workaround is to enter $4000 less than the actual box 1 amount, when you enter the 1098-T on the student's return or $4000 more in the box 5 amount.
* From the 2019 form 1040 instructions (pg 95): “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040, line 18c, and IRS.gov/EdCredit. Page 16 of PUB 970 (2019) actually has examples of how to do the “loop hole”.
