Welcome to the Forum!!!
I can't give you any advice specific to children
, but I will say that the cruising lifestyle present a great opportunity to open and expand the mind by visiting different locals and meeting new people and cultures.
From the preliminary research
I've done, home schooling seems to be a viable, if not better experience fr children
. If you're concerned with their ability to make fiends and socialize, it shouldn't be a problem. Additionally, you'll have the ability to spend more time and better influence the course of their development.
As it stands, and forgive me if I'm getting political, public schools are dropping their standard in this county and private schools are becoming more and more expensive and may be pushing an agenda/academic program, which may be contrary to what a parent may want.
There is a group here on sailing with children. they may have better advice and experience on what you will need.