Thanks for clarifying the question a bit more. If you itemized, and included the California taxes as part of your deductions last year, you do have to include all 1000 of the refund as potentially taxable this year for Federal. (If you did not itemize, then you do not need to report it at all). Then, as part of your itemized deduction for this year (2018), you would include the 800 payment you made to KY LAST year (for 2017, and you unfortunately cannot include the 100 penalty for this deduction).
This is the way that this portion must be claimed, but, of course, the bad news is that the change in law with TCJA makes it less likely you'll get any benefit from claiming the KY tax you had to repay.
Having said this, I strongly recommend that you speak to the company and see if they can withhold for KY. If they cannot, make estimated payments. In either case, have them stop withholding California. You are paying those taxes needlessly.
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