Is there any way to see how the state tax refund includeable in taxable federal income is being taxed? I'm coming up with a different number.

Tax is not calculated separately on different parts of your income. The tax is calculated on your total taxable income.

What you could do is, after you have entered all of your income, temporarily delete the state tax refund and see how much your total tax changes. Make sure you put the state tax refund back in before you file.

Review all the worksheets ...  

Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.  

Choose the option Include government and TurboTax worksheets