I am serving on active duty in the military. My wife (civilian) and I have our state of residence as Pennsylvania. The daycare that she worked at for 3/4 of the year was taking out NC state tax. The daycare that she worked for for the remainder of th

You will have to file a non-resident NC tax return to get a refund of any NC tax withheld by your wife's NC employers. 

Going forward, make sure her NC employers know she is exempt from NC withholding by completing NC Form NC4 (http://www.dornc.com/downloads/nc4.pdf)

Active-duty military and their spouses are considered to live in their state HOR no matter where they are stationed. Their active-duty pay and spouse's local income are considered to be earned in their state HOR. 

When you complete the Personal Interview:

1. Select Pennsylvania as your state of residence (both of you);
2. Answer "No" when asked if you "Lived in another state in 2016?" (both of you) That question only applies if you changed your state of residence in 2016.
3. When asked if you "Earned money in another state?", answer "No" (unless the military member had non-military income in NC)