I don't understand what is being missed here and it could be me.
Home schools are explicitly exempted from weapon prohibitions. If children are in your home, you already should be meeting state regulations on keeping them safe or under your direct control at all times (in a holster for example or locked up in a safe).
There is no need for a firearms curriculum (JUST) so you can justify having the gun there. Of course, you should be teaching your kids about guns anyway.
The exemption is here (g)#3:
Home schools are defined here, under Part 3.
I think the main difference between private schools and home schools is that private schools are looked at more as corporate/chartered educational properties, such as colleges and universities. Mainly due to the fact that they may have quite a few children to instruct. Home schools are meant to be very small and involve just the children of a couple of families or households as defined in the general statutes.