TN does not have an income tax. If her intent is to remain in TN, she is now a TN resident. She files as a part year resident of VA and files a non resident SC return. Prepare the SC return first. VA will give her a credit for tax paid to SC.
If she considers her time in TN as temporary and intends to return to VA, then she is a full year resident of VA. This means that her TN will be taxed by VA. She files a VA resident return and a SC non resident return. Again, prepare the SC return 1st.
"A dependent student is a resident of the state in which the Taxpayer that claims the student lives." So, for her time in SC, she is still considered a VA resident. But, that rule changes slightly once she is no longer a student. As a dependent, she is still considered as living with you, if her time in TN is intended to be temporary. Put another way, she can still be your "Qualifying Child Dependent even if she is a part year resident of TN. This is because she is considered as having lived with you for more than half the year (January to August)
