My medical insurance allows my daughter, now 19, to stay on as a
covered dependent only if she's a fulltime student. But she needs to
drop out of school in order to do residential drug-abuse therapy. I'd
like to learn more about how to play the system to keep her coverage
going: can she go on medical leave of absence (or some such) and have
that satisfy the insurer? are there any laws preventing the insurers
from cutting her off, when this is a medical necessity? does HIPAA
offer me any recourse?

I think that, given her medical history, it would be hard to get
individual coverage for her if she loses her group coverage with me.
What sort of professional might be able to advise me the best way to
navigate the shoals of HIPAA, COBRA, and the health insurance
companies?

The COBRA question is simple, she is not eligble. 
Some states require insurance companies to insure all people at the
same price. Check with your state's insurance regulation department.
Also, check to see if she can get on state subsidized insurance.

and my advice would be to start with a social worker at a community
service agency if you can find one.
Josh