Blue Cross/Blue Shield is a national organization, but there are individual state or regional branches. For instance I'm a CA resident covered by Blue Cross CA. I went skiing in Utah, hurt my ankle, and went to an urgent care clinic in UT for an x-ray. When I got back I called my insurance office and they said that I was covered, but since I was out of state at the time of the injury, the clinic should bill the *Utah* Blue Cross. This seemed odd to me, and also to the billing person at the clinic when I called them, but it all seemed to work out OK. But the NY BC/BS might not want to cover you if they consider you a resident of PA (not necessarily related to whether your school considers you a resident).
There are a lot of state-to-state commuters in the northeast - people who live in NJ or DE and work in PA, people in NJ or CT that work in NY, etc., and insurance companies expect that. I lived in DE and worked in PA for a while, and my insurance plan had providers in DE. But this is limited to what they consider a normal state-to-state commute distance. There are four regional BC/BS companies in NY state, and not all of them have providers in PA.
So I think you need to do the following:
1. Find out what your family's business' actual insurance company is.
2. Call them and ask if they'll still cover you if you're living in PA, possibly depending on whether
a) they consider you a resident of PA, or
b) they consider you a resident of NY (e.g. if you continue to file NY tax returns and maintain a permanant address in NY).
If they'll cover you, and they have providers in your area of PA, you're golden. If they'll cover you as a NY resident but don't have providers in PA, you might need to designate a primary care provider in NY, and then every time you need medical care in PA you'll be going to an "out of state" provider and probably subject to the hooplah I mentioned above. The BC/BS local to where you live in PA might eventually take exception to that, since they're not getting your premiums.
