Can I receive travel reimbursement as a respite care provider to a diaplegic child with spinal bifida. I receive paid income reported on a W-2

Travel reimbursement comes from your employer. Some states allow a deduction for unreimbursed employee expenses on the state return, IF you are itemizing.

There is no federal deduction (starting in 2018) for job expenses of W-2 employees, including mileage.