The 1099-Q goes on your tax return with your daughter's 1098-T, as KrisD15 advised. When you enter the 1099-Q you will get a question about "who is the recipient" and "who is the beneficiary". In your case, for both questions it is your daughter.
The issue with your AOTC amount is that TurboTax assumes you want to use the 1099-Q amount first . But, you probably want to first use your daughter's qualified education expenses for the AOTC first, with any additional qualified expenses applied toward the 1099-Q distribution. The easiest way to fix this in your Download/CD version of TurboTax is to go to Forms mode and find your daughter's "Student Info Wk". Scroll down to Part VI and find line 17. If you enter $4,000 on line 17, TurboTax will first use $4,000 of your daughter's qualified expenses for the education credits/deductions (e.g., AOTC) and then use the rest of the expenses you entered to apply against the 1099-Q distribution.
Note that if you enter the 1099-Q first (or whenever you enter it), TurboTax will open up boxes in the 1098-T section for you to enter any room and board and other types of expenses that can be used for the 1099-Q distribution, but not the AOTC.
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