I'm assuming your wife is a Japanese citizen. If so, she can come to Canada as a visitor without a visa. The children are Canadian citizens (probably), so if they are traveling on Canadian passports there will be no problem. If they are traveling on Japanese passports, they can also come to Canada without a visa.
When your wife enters Canada, she should be clear that she is just visiting. The border agent may ask for proof of ties to Japan: things like a return ticket, a lease, a bank account, a job in Japan, etc. If she doesn't have proof of ties, it is a good idea to at least get a return ticket.
Many people have entered Canada as a visitor when their plan was to apply for a PR visa, and for people who can enter Canada without a visa, there is usually no problem. One way to make it less worrying is to send in the application before she arrives in Canada. She can then show proof of the PR application to the border agent if asked: proof could be the fee receipt, or the letter accepting you as a sponsor. You can even pay early, get the fee receipt, then not actually send in the forms until after she has arrived. However, she should still be clear that she is just visiting, and will leave Canada if her PR visa application is rejected (which would be very unlikely).
Once she is in Canada, you can apply either inland or outland. Inland means the application is processed in Canada: it usually takes longer than outland, and is not really necessary for someone with a visa-free entry. Outland means the application is processed outside of Canada, in Manila now (I think) for Japanese applicants. Lots of forum members have applied outland while visiting their spouse in Canada, and everything is usually fine. If there is an interview, for outland your wife would have to go to Japan for it; however, if you submit a good application and your relationship has no 'red flags', she would probably not be called for an interview, since you have lived together and have children.