My husband lives and works in VA due to aging parent. I live and work in SC with our 17 year old due to aging parent. I travel to VA every month for weekend. We file joint on Federal but how do I file with the states?

On VA tax return your husband is resident and will report all his income. You are nonresident and do not have any VA income.
Similar approach for SC. Your U.S. Tax Return: Working or Living in Two or More states

You can each file as Married Filing Separately in your separate states. This lets you avoid having to report your income to VA, or your husband's income to SC. You can file this way for the two states and still file as Married Filing Jointly on your federal return as long as you have no VA income at all, and your husband has no SC at all, and neither of you actually lived in the other's state in 2009.