@fbrackin1960
No, the two items don’t cancel each other out in that way, they are treated separately. On your 2019 tax return, you deducted the state taxes that you actually paid in 2019, this is usually your withholding. If you paid additional tax to state #2 in 2020, that is a tax deduction for 2020. You list it as an itemized deduction for 2020.
If you got a refund from state #1 in 2020, that may or may not be taxable income on your 2020 tax return depending on the tax benefit rule. You have to analyze whether your overall itemized deductions for 2019 would have been less if you removed the amount of the state tax refund. If you find that your deduction would have been less on schedule A with a reduced tax amount, that means you got a tax benefit in 2019 which means the refund is taxable in 2020.
