You are correct, your tax rate does not change. For each child's Form 8615, it is taking into account the income from all other children and yourself. The calculation is based on the parent's income so that each child is being taxed at the parent's tax rate for their own income.
As you work through the form in Part II, the child's income/tax is used against all income to arrive at their percentage of income to check the tax using the child's filing status. In the end each child is paying their portion of the tax as if the income was being reported on your tax return.
If you qualify you could include the income on your tax return using Form 8814. This is allowed if their only income is from interest and dividends and the tax would be the same. All income would be reported on your tax return. The total tax results will not change.
You can review your printed return if you have doubts before you file, after payment.
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