It took us a couple of months to get all the papers together since ordering police certificates and getting stuff translated and getting an appointment for a medical all took time. I don't imagine it's possible to get PR in three months.
From what I've read on this forum, your wife can visit you while her outland PR application is in process (or even arrive as a visitor and then file "outland"), as KL8N suggests, so perhaps you can move back "alone" and she can "visit" with a round-trip ticket, and keep extending her visitor's visa during the waiting time (no guarantee they would be granted, of course), and if they did request an interview she would have to fly back for that. Once PR is approved the visa office needs to put the visa in the passport, I believe some people mail their passports to their foreign VO from Canada. I guess she would need to keep some address in Japan though, I'm not sure how this works exactly but there seem to be plenty of people on this forum already living in Canada on visitor's visas while applying outland. Also, re the interview: Not everyone is required to do an interview, I gather from what I'm reading that certain regions/Visa Offices and certain types of relationships (probably the more complicated ones) would almost guarantee she would be interviewed. If you are worried about it, you can search this forum or maybe check trackitt.com.
As KL8N says, I guess the risk would be that when they arrive to "visit", the immigration can refuse her if they believe she won't leave the country again. I suppose that is not as likely in the case of Japanese citizens because moving from Japan to Canada wouldn't be considered as an improvement in standard of living/rights and freedoms, etc. Once again, there should be people on here who have done this, hopefully they can advise you (or you can search the forum). You could always move there and apply inland (takes way longer) if there is no hurry for your wife to work and you don't mind not being able to leave the country for a while. Although applying inland has other disadvantages, like probably you'd have no health care coverage until they get PR and there's no right of appeal if the application is refused.
I've no idea whether your kids would be allowed to go to school without their papers, although I'm guessing they would since there seem to be plenty of people in more precarious/illegal situations than that who's kids are in school - that's something you could check into quite easily if you already own a house, just call the applicable local school.
Good luck!
TLH
