If she is a W-2 employee, she can deduct any unreimbursed work expenses like any other employee deducts work expenses, using form 2106, which becomes an itemized deduction on schedule A subject to the 2% rule. This would include classroom supplies and other expenses, and mileage driving between the two work sites if she works at both sites on the same day. (Mileage from home to the first site of the day and mileage from the last site of the day to home is non-deductible commuting.)
Additionally, the first $250 of expenses can be a special top line teacher deduction if she qualifies. Teaching college does not qualify, but the private academy might if it is K-12.
https://www.irs.gov/taxtopics/tc450/tc458
