To elaborate on Mike's reply..................
Work visas require a college degree (not technical school). As Mike wrote, you apply for the job, and after you are accepted,
then you apply for the work visa (along with the employer, who must provide documentation to prove he is a valid one and has a contract for you).
JET program doesn't take people without college degrees, either.
The certifications you have are nice enough, but I don't recall 4 years being enough to override the lack of a college degree. You
might want to contact an immigration lawyer to see if he thinks it's feasible to combine a 2-year tech degree with 4 years of work as an equivalent substitute. If so, and you are successful, you could take your wife here on a dependent visa, and she could work part-time wherever someone felt she is suitable. To be honest, even with a dep. visa in her hand, I don't think most employers even in the teaching field of eikaiwa would look twice at her. Just not enough education even though the dep. visa makes her legal. You never know, though.
Also, she should keep in mind (and you, too, since you indicated you'd also be willing to get teaching work prior to a job in your field) that teaching English may sound like a piece of cake, but it's actual
work. I taught eikaiwa for 4 years, then HS for another 4, and since then I've been at a university for almost 12 years, all teaching English. The eikaiwa gigs are paying lower and lower now. Get on the
ESL Cafe website and ask the teachers and wannabes there for the most up to date on the ground status on such work. It's pretty pitiful as far as I know in terms of money.
But unless
you get lucky with immigration for work in your field,
you're not going to get a teaching job.
Just curious...how old are each of you? And, do you have a timeline for coming here? And, why Japan?
Mike asked about your Japanese skills, and you said "We plan to learn Japanese before moving." Uh, that's too vague. Speaking, reading, writing, and to what level? I added my question above about timelines to address Mike's (unanswered) question about when you plan to come, by the way.