You can ignore the 1099-Q. Box 1 is fully covered by Room & Board. The 1099-Q does not need to be entered and shouldn't be entered. As you know, it just makes the calculations more difficult.
On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution."
As you surmised, you can claim the AOTC on your return. The simplest way is to enter the 1098-T with $4000 in box 1 and 0 in box 5. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. What you enter is not sent to the IRS; it's just used for calculations.
$29,979 Tuition & Fess
+ 1,500 Books & computers
- 4,000 Used by the parent for AOTC
=$27,479 Qualified expenses for the Scholarship
$32,695 Total Scholarship
- 27,479 Qual. Expenses
= 5,216 of the Scholarship is taxable
Technically, she does not even have to file a tax return ($700 + 5216 = 5916 < $12,550 filing requirement). You may want to have her file just to document that the taxable scholarship was reported (freeing up $4000 tuition for the AOTC). The simple way is to enter the 1098-T with 0 in box 1 and $5216 in box 5.
