Enter the 1098-T on your return. Ignore the 1099-Q, on your return. When you get done TurboTax (TT) will give you the AOTC and indicate that $4000 was used to claim the credit.
When you do her return, enter the 1099-Q first. Then enter the 1098-T. You will eventually reach the screen "amount used to claim the education credit". If TT has not prepopulated that with $4000, you should enter (or change to) $4000.
TT will not try to give the tuition credit to your daughter, on her return, if you indicate, in the personal info section, that she is claimed as your dependent.
For a full explanation read on (but it appears you already understand the specifics)
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For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the 1099-Q can be either the owner or the beneficiary depending on where the money was sent. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient".
The 1099-Q gets reported on the recipient's return. The recipient's name & SSN will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.
You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit, that gets him an exclusion from the taxability of the earnings (interest) on the QTP. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (not yours), but not the penalty.
Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q.
Example:
$10,000 in educational expenses(including room & board)
-$3000 paid by tax free scholarship
-$4000 used to claim the American Opportunity credit
=$3000 Can be used against the 1099-Q (usually on the student’s return)
Box 1 of the 1099-Q is $5000
Box 2 is $600
3000/5000=60% of the earnings are tax free
60%x600= $360
You have $240 of taxable income (600-360)
http://turbotax.intuit.com/support/iq/Education/Information-about-Form-1099-Q/GEN12272.html
