I too, have the same situation as your wife does only a little different. Work in DE, live in PA. My company does not withhold PA income tax and only sends one W2 and only withholds for DE.
Yes, you do need/should to file in both states.
I typically file in DE on their website. Its free.
I use Turbo Tax +state to prepare my PA taxes and then mail them in because I paid DE income taxes (which is also higher than PA) You should file in DE first then PA will/should recognize the taxes your wife paid in DE.
Good luck
V
