From the info supplied the child is a qualifying person for the TP to file HH, enter the childs name and SS on line 4 federal information sheet. AOTC? That is another questtion since the kid would have to check the box "can TP be claimed as a dependent of another TP such as parent.
As Camp said, "yes", but the child would only be qualified for the "non-refundable" portion of the American Opportunity Credit.
There is a theoretical circumstance where the child has earned income more than 1/2 of their support but it was put in savings instead of spent on support, thus allowing refundable AOTC. I've personally never seen such a unicorn though.
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