If the assignment lasts more than 1 year, your employer is not allowed to provide you tax free reimbursement of expenses. So, yes the reimbursement is taxable income to you. The fact that your work in VA is intermittent may negate the one year rule. So, it really depends on how your employer treats the reimbursement. If they report it as taxable income, on your W-2, you're probably stuck with that. If they don't, you can probably get away with not reporting it.
As for state taxes; you are an NC resident and will file an NC return and pay (calculate) NC tax on all your income. You will file a non-resident VA return and pay only tax on your VA income. You will have to keep track of the days worked in each state. NC will give you a credit, or partial credit, for any tax you pay to VA. So there will be little or no double taxation. Due to the fact that your W-2 will report all your salary as VA source income, you may may get some kick back from VA, if you report less.
