I have 3 children, and received $0 of the hybrid tax credit too. Boy was I steamed!

Even though I didn't qualify for AMT, your AMT tax basis is a floor for how low your hybrid tax credit can reduce your tax basis. Other credits do not use your AMT tax basis as a floor, so it appears to be unique to the hybrid credit.

I did sell a small amount of stock this year, but if I didn't have the $3000 credit for my kids I would have received the entire hybrid tax credit. If I hadn't sold any stock, I would have maybe received ~$400 of the credit.

It IS a child unfriendly credit.