I am wondering if there is a special type of Visa that enables you to take your wife and son with you in Japan while you work?
Is there a visa that can enable you to take your non-Japanese wife and children to Japan while you work?
With a normal working visa, your spouse and dependent children are eligible for a Dependent visa.
After obtaining that visa, your spouse can apply for permission to work up to 28 hours a week. Should they meet the requirements for a working visa and find a full time position, they can of course apply for that as well.
If you have the Highly Skilled Professional visa, your spouse can work full time.
I would like to share this website as well. It provides useful resources about visa categories and procedures in Japan.