I would not. I think you have things confused. Any scholarship income not used on tuition is taxable. The tax on scholarship income is preferable to the 1099-Q. You want to reduce the 1099-Q as much as possible. Keep your paperwork showing how you did the math. If the scholarship has restrictions that it must be used on tuition, you must. Most scholarships can be used for living expenses and are much better for taxation.
Parent return: $65380 of expenses, Q is $66,294 so you have a very little taxable Q income on your return plus the education credit.
Student return: the entire scholarship is taxable income. It may turn out that the education credit is not worth it by the time you add the extra income plus kiddie tax. See What is the Kiddie Tax?
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