The requirements depend on the state where you live. Some states only require a certain number of days/hours per year with a basic core content of curriculum (most "canned" curriculi meet these standards), an attendance record, etc. Other states have stricter requirements.
As far as having to know each and every subject inside and out in order to teach it.... I respectfully disagree. At high school age, your child is fully capable of being handed a particular packet of information, doing the lessons, reading, and research, and being self motivated enough (and if she isn't, this can be a great lesson as well) to move ahead with learning the content of that packet. Because most lessons will include an introduction, the content, and a summary/test, you can learn right along with her. Do I remember my Physics II class from high school? No. But when the time comes, I will learn right along with my son, he will learn it with me, and on his own.
During a typical school day in a public school, if the child is there for 7 hours, approximately 1 hour is spent on administrative type stuff from the teachers---attendance, announcements, paper-handing-out, etc, times 5 or 6 teachers!! Another 30 minutes is spent getting from one place to another, at least! Actual instruction time is probably only 20-25 minutes in each class, and because of different learning styles of the students, what could be taught in half the time is stretched out so that everyone gets it. We are able to get through our lessons in a much shorter time period, and then there is time for my son to study what he is interested in---architecture, history, and engineering. We are able to gear his studies towards what he wants to do.
It's a very personal decision. I HS my son, but my daughter attends a public school---they have very different learning styles, my daughter does great in the traditional setting of auditory/sequential learning, she's an honor student and gets straight A's every year. My son, however, is more of a visual/spatial learner and would do terrible in a school setting, I am more able to teach him, according to his style, at home. A lot of soul searching, in my opinion, is needed prior to making such an important decision.
Good luck!