I don't want to pry, but your legal situation will vary wildly depending on your answer: Where I come from "partner" implies that you are not in a heterosexual relationship and you are not married. If this is the case, you've got a huge hurdle in front of you. Is this the case?
Also, keep in mind homeschooling isn't really a viable option in Japan, but private schools (despite being costly) are. Sorry to be a bit of a bummer here.