Over here, what your church is doing would be called a private school. On the other hand, we sometimes organize into groups that we call co-ops (for cooperative, as in a cooperative effort). We used to be involved with one wherein each parent would teach a subject that they were strong in to more than their own children (I taught math and science). Frankly, I think it was more of a comfort to the parents who were worried about subjects they weren't "good at" than it was beneficial to the children being taught.

P.S. I'm very impressed that you picked up on the use of the wrong term (principle instead of principal) in my previous post. Where, or perhaps when, were you educated?