You can enter both 1098-T's for both schools in the Education Section. TurboTax will add both Box 1 amounts and Box 5 amounts together, so you will still have plenty of Education Expenses left to claim education credits, and not have any taxable scholarship income.
Here's instructions on How to Enter a 1098-T.
You may have to upgrade to Deluxe from the Free version, but TurboTax will let you know as soon as you enter anything not covered in the Free version, and you upgrade immediately (and painlessly).
She won't have to file a tax return in a non-resident state, unless she paid tax there and wants a refund.
Here's more info on How to File a Non-Resident State Return.
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