I think people are misunderstanding - I read OP’s post to say that her kid is homeschooled and is taking the AP class through a private online program. Many homeschooled students do this and it would not disqualify the kid from taking the AP exam at the FCPS base school.

That’s the issue. OP is not a registered homeschooler so the county has no obligation to provide a seat for exams. She also is not a homeschooler so asking HEAV is not appropriate. OP, what does your private online school say you should do?