You have to look at the forms.
I believe (but haven't tested it) that the credit for other dependents is applied before the education credit.
The American Opportunity Tax credit (AOTC) comes in two parts, refundable (line 18c of form 1040) and non refundable (line 3 of Schedule 3, then to 13b of form 1040). If the non refundable credit is limited by your tax liability, TT will complete a Credit Limit Worksheet before entering an amount on line 19 of form 8863. That amounts goes to line 3 of Schedule 3.
