Should I amend 2014 & 2015 returns to remove American Opportunity (8863) credit to get much better credit in 2018 & 2019 instead?

My daughter took some college courses while in high school. The American Opportunity credit (see form 8863) in those years was much smaller than the credit would be now that she's enrolled full-time.

I'm wondering if I should amend 2014 & 2015 returns, to remove the American Opportunity credit in those years, so that I can use it during 2018 & 2019. Realizing that I will pay more taxes on the amended returns, but much less on the new returns because the credit is drastically (~$2-3k) larger now. She will still qualify as a full-time student working towards a bachelor's degree.

Is it okay to amend 2014? I read somewhere that 3 years was the rule of thumb. Are there audit risks with amending? Does this plan work for the American Opportunity credit?

Thank you!