So there is a couple of things. When does their present visa expire? The theory is, even if you apply the night before, as long as they have not expired, you will have implied status until they "decide".
That said, you have been granted AIP. So you can apply to work (which I suspect you would have to apply to restore status on the same OWP application -- $200 more -- they can return this if unnecessary).
So, WRT children, see:
http://www.cic.gc.ca/english/study/study-minors.asp :
"
Exceptions: Studying without a study permit
In some cases, minor children do not need a study permit to study in Canada. These cases include:
- minor children attending kindergarten;
- minor children who are refugees or refugee claimants, or whose parents are refugees or refugee claimants; and
- minor children who are already in Canada with parents who are allowed to work or study in Canada, and who want to attend pre-school, primary or secondary school.
When minor children studying in Canada without a permit reach the age of majority (turn 18 or 19 depending on the province or territory), they must apply for a permit if they want to continue studying.
"
So, you can either correct your status, or continue theirs. They would be eligible for schooling in either case.
If you continue theirs, as long as they receive the application(s) the day before the present permit expires, they would have implied student status (means they can continue to attend school until CIC "decides").
Not sure how much that helps....
