We have been living in Europe on a job assignment, which was supposed to last 5 years.
Before leaving the States, we sold our home in PA. Last year, we built a home in SC, near to family, with the idea that we would retire there when we return in 5 years. We are now returning to the States next month. We are having all of our belongings shipped to SC as that is the only home we own.
My husband, however, will return to work in PA for the next 3 years, and I most likely will find a job there also to be with him. We will have a small apartment in PA in order to do this. We hope to spend time off in SC as much as possible.
It sounds like, from a previous post, that we will need to establish residency in PA, along with registering our car there? And so, do we also pay our federal and state income taxes in PA?
What happens about our house in SC? Will we be taxed as nonresidents? Will that house be considered a vacation house even though we own no other property and we consider it our home? Does having a "vacation" house increase federal tax burden? Other than property taxes, will we need to pay any other taxes to SC?
Thanks for your help, as this is complicated.

1. If you work in a state (irrespective of you have house or car registered in the state), you must file tax return reporting income earned while in the state.
2. The state you live and worked for the major part of your year (irrespective of you have house or car registered in the state), is normally your tax home.
3. In the state that is your tax home, you report your income for the year even earned and reported in other states. But if you paid taxes to any other state, you will claim credit for it in your home state tax return.

Your state of residence is the state where you spend the most nights, irrespective of whether you work in that state or not. So if you are going to spend the majority of nights in PA, then PA will be your home state for tax purposes. If this is the case, you will not owe SC any income tax (assuming you have no SC source of income), although you will of course have to pay real estate tax on your SC home. To keep things simple I would suggest that you and your husband use the PA apartment as the home address for payroll purposes. As for registering the car in PA - that has nothing to do with establishing tax residency, but I suspect that PA (like most states) has a rule requiring new residents to register cars in state within some period (typically 30 days). You would also get your PA driver's licenses at the same time. Finally, yes, you can think of the SC residence as your vacation home. There are no extra tax burdens for owning a second home other than the real estate taxes you pay to the SC municipality - you can deduct mortgage interest and real estate taxes for two homes on your federal taxes.