Haven't read through all six pages, so maybe I missed it, but how old are your
kids?
Someone made a good point about
kids needing the socialization of in person
school and the idea that they can be home schooled at sea, then dropped into a HS might be a bad one.
You've already taken the plunge, so congrats on your
new boat.
My
advice would be to go ahead with this lifestyle while your kids are young, but do make extended stays in areas where your kids can develop friendships with others.
But I would look at settling somewhere longterm by the time your kids are in 3-4th grade. Doesn't mean you can't still
liveaboard. Maybe do it in PR, VIs, maybe somewhere in southern US.
This would allow your kids to have a normal
school experience and you still get to do a good bit of sailing.