I have paid all my children's educational expenses this year with their 529 plans. Is it possible for me to pay the taxes on $4000 or more of my qualified withdrawals from the 529 plan so that I can take the American Opportunity Tax Credit? If I did this I would not be double dipping and would seem like I could take the credit. My tax rate is low. Is this allowed?
Yes, this is allowed (call it a loophole, if you like). You can choose to designate expenses towards credits/deductions (there is a question about this in the TurboTax interview), thereby making the 529 distribution taxable if there are not sufficient additional education expenses to offset it.
The taxable 529 distributions should be reported on your children's tax returns.