What you are writing about is called HomeSchool.
I urge you to find and link up with a co-op or local group of folks who also HomeSchool. You will discover wonderful synergy and support in such a group.
Also, I urge you to find and attend a local HomeSchool convention/meeting/curriculum event. You will be astounded at the marvelous resources that are available.
No, it isn't home schooling. It is a proprietary Charter school to which tax funds are diverted based on enrollment.
No, this is not home school (I’m all for homeschooling, unfortunately, it’s just not practical for us). This is a Texas public school, conducted online. The courses are self paced, with only the ending date being specified, and they are tailored to the individual child. I expect to see my kid burn through them quickly.