Yes, I believe you can, and should, amend both your 2014 and 2015 federal income tax returns, surrendering your claim of the American Opportunity Tax Credit with respect to your daughter for those two years.
While you are correct that the general rule is that an income tax return cannot be amended more than the later of three years after its due date or two years after the tax was paid, that applies only to amendments which include a claim for a credit or refund. Since you will be voluntarily amending to pay more tax for those years, the time limit does not apply. Amending a return does not automatically trigger an audit or necessarily increase your chance of audit selection.
I think there exists a valid argument that you may have taken the AOTC in good faith, but in error, for 2014 and 2015. One of the requirements for the AOTC is that the student be enrolled at least half-time in a program leading to a degree. Most high school students who take college courses are not carrying a half-time college credit load, nor are they yet formally enrolled in a degree-granting program. If your daughter was in that situation, she did not meet the qualifications for the AOTC. That will be your stated reason for amending the returns.
Please be aware that the IRS processes Forms 1040X slowly. It may take as much as ten weeks for an amendment to be reflected in your tax records. For this reason, I would suggest that you wait as long as possible, yet within the filing deadline of April 15, to file your 2018 tax return, to minimize the possibility that the IRS will generate a notice that you have claimed the AOTC for more than four years for your student.
