It's likely that the increase in your AGI caused by the IRA distribution is reducing your child tax credit and explains most of the difference between the tax bracket rate and the marginal tax rate, increasing your marginal tax rate above the tax-bracket rate. The effect is most pronounced with lower distribution amounts. A reduction in some tax credit is one of the things I suggested in my original post.
It's side effects like this that make it necessary to simulate your entire tax return. Because the there is less marginal reduction in the child tax credit as AGI goes up, you might find that it makes sense to take larger distributions over fewer years, but it depends on the ages of your children which affects how many more years you will receive this tax credit.
Note that there are changes to (reductions in) the child tax credit for 2022. Given that 2022 TurboTax does not yet support the entry of Forms 1099-R in step-by-step mode, I suspect that you are simulating a 2022 tax return with 2021 TurboTax. To get accurate results, you would need to simulate your tax return using forms mode of 2022 TurboTax. I think that these changes in the child tax credit for 2022 will cause a reduction in the calculated marginal tax rates compared to doing the same simulation in 2021 TurboTax.
Having only 22% withheld for federal tax is unlikely to be sufficient to avoid a significant balance due when you file.
