Tax Year Prior to 2020: I got married in 2016 and so our 2015 returns were file separately of course. Can I show my 2015 state refund on our 2016 1040 as taxable and my wife's as non taxable?

I got married in 2016.  In 2015, my fiance took the standard deduction while I itemized on my federal return.  Since I deducted my state taxes on the 2015 Schedule A, I need to report it as taxable income on our joint 2016 return. My wife didn't deduct her state taxes in 2015, do I have to include here 2015 1099-G state tax return amount  with mine as taxable or is there a way to separate the 2?

Retirement tax questions

Yes. If she did not itemize in 2015, you will simply exclude her 1099-G form from reporting.  The IRS will have a record of whether or not she itemized in 2015 so there should not be an issue with that.