A qualified dividend is an ordinary dividend that can be reported to the IRS as a capital gain rather than as ordinary income.
In other words, all dividends are ordinary dividends, but not all dividends are qualified dividends. Therefore your qualified dividends are never more than your ordinary dividends.
You will also never see a 1099-DIV where the qualified dividends in box 1b are more than the ordinary dividends in box 1a.
If you think your are being taxed twice, you are not understanding the Qualified Dividends and Long Term Gains (QDLTG) worksheet. That worksheet separates your qualified dividends and net long term gains from the rest of your income and calculates a special income tax rate for them that is as low as 0%.
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