Here’s another question for you: “Is it ever right for a church elder board to dictate (or insist upon) how a family is to educate their child(ren)?”
The answer to this query is, “No.” Issues of this sort are to be left up to the family. This is why it is wrong for some sessions to limit the membership of an elder board to those (only) who refuse to send their children to public schools. The elders have no right to do this.
It is intriguing to me personally, that many people who fear that the government, or the church will come in and take their children away from them, and will insist in educating them in some other form than the family has chosen—are the very ones, on the other hand, who are quick to draw the conclusion that state (and sometimes even private school education) is unacceptable, (and that responsible Christians would never do this).
You cannot have it both ways. Fierceness of conviction, (which sometimes leads to idolatry), cannot be translated into uniformity of practice among others. You are not permitted to do to others, what you fear others will do to you, (cf. Matt. 7:12).
So, elder boards are wise to leave issues of these sorts to the discretion of the families under their spiritual jurisdiction.