What province may also have an impact. Schools are not immigration experts so proof required can vary and schools may not be familiar with provincial policies.
Yes. It does matter what province especially, and it may be useful to look up the provincial regulations.
I'd also note: if you ask schools the most general question, they'll likely give you the canned answer that someone has written somewhere (for easy reference, not the complicated answers) eg 'show us your PR card.'
Sometimes one does have to push back, ask again, ask for the written rules, speak to a manager, look things up and show them, etc. The admissions office will not know everythign the finance office does, and the front-line 'call centre' people in any department probably don't know the details. And you probably can't get these detailed answers dealt with as a hypothetical - it has to be for a specific case (eg a student who's already been admitted).
Other thing:
@NomadPR, you haven't updated, told us whether the kids are now in Canada, age, or the school, or anything. We just can't know the answers.
Even if you do provide that stuff - you're probably going to have to deal with it yourself. Your story above is ... messy. People here can give hints and info about what they know, but it's still on you to deal with it.