Either you pay that tax to KY or to Indiana but not to both. I agree with your version of it, that you are correct in filing a part-year return through allocating your income. Your company cannot supply you with a corrected W2 because they withheld KY tax on (XX) income. They can't un-report that.
I believe that if you can show proof of residency to KY (change of move and residency to Indiana), that KY should respect your allocations. If you renewed your driver's license with Indiana, have a lease contract you can show them, or something else similar, they will split the income. (KY and Indiana are reciprocal states but part-year situations are not technically covered by reciprocity).
If this does not work with KY, then your next option is to file an amended Indiana part-year return. In this case, you will claim a credit on the return for the taxes you paid to KY while living in Indiana, and get back the Indiana taxes you just paid at least. You would supply Indiana a copy of the KY return showing that you must claim all of the income to KY.
Either way, you don't pay taxes to both. You either get back the KY portion from KY, or you get back the taxes you paid to Indiana.
Going forward, you pay state taxes to Indiana. If you are working in KY and pay a local tax in KY, you will be able to claim a credit on the Indiana return for KY local taxes. That will be next year. Feel free to comment back if I can assist you further with this year.
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