Actually, going to Japan is a lot easier for Americans than us here in Serbia. The best way is to go through a student exchange program, as I did, so you could get paid for going there, fare and all. :) If you are a student, ask if your Uni has such a program. As I saw on two separate occasions, most of the University dorms in Japan are equipped with a few rooms for families.
If you're not a student, however, there still are many ways for you to go there. In Japan they love people whose native language is English and local international exchange organizations would provide you with a part-time job of teaching English and what not.
Just wanted to tell you it's not impossible, but because you have a family, a lot of thinking about the priorities would be necessary if you intend to stay there for a year or so. :) Any further questions? Send them to my inbox.
