KY State and Local Taxes for Working Remotely

Hello,

Last year we moved from KY to VA. My wife had a job in KY and used to commute to her office but then started working remotely from VA. So We are now filing part-year resident tax for both VA and KY. Her employer however kept withholding KY tax as her role was initially defined as in-person job (not remote). Here's my couple questions:
1- how should we file KY state tax?
    a) take only portion of the income for KY and the rest for VA; or,
    b) all the income taxable for KY for the whole year, but then we take that paid tax to KY as credit for VA?

2- If the answer to the question above is "a)", can we file a return for the local taxes paid to Louisville/Jefferson County (where we lived) to get back a portion of what was paid?