I have quoted the previous post again because of the discrepancy in who this is about. You? Or your sister? Makes no difference to me but it makes it more difficult to sort through things.
In addition, you posted similar queries in another part of the forum, and for which you got very good responses from
@scylla, who appears to be keeping better track of ongoing developments in a range of matters well beyond what I do.
I cut back my activity here a number of years ago to focus on a few issues; PR Residency Obligation issues is among those I still follow, and in doing so I have indirect exposure to ongoing developments in related matters, like PRs with RO issues who want to sponsor children or partners. But I do not keep up with the details affecting sponsoring dependents.
In any event, again my impression is you already received some good responses from
@scylla . . . for example this one:
IN TERMS OF YOU PERSONALLY UPON ARRIVAL IN CANADA:
Apart from the complications about how to bring your children, when, sponsoring them for permanent status, and providing a life for them in Canada, you have identified some key elements involved in just YOU coming and settling in Canada, and in particular the impact of having an expired PR card on things like applying for and obtaining government insured health care coverage, and the process for "PR card renewal."
As I have said, and as
@scylla responded a number of weeks ago, the PR TD issued for H&C reasons means (as long as the PR TD is valid) you can board transportation destined for Canada (of course you also need a valid passport) and upon arrival you SHOULD then be allowed to enter Canada without being reported for not meeting the Residency Obligation. And, moreover, you should be able to promptly apply for a new PR card. Most PRs who have failed to meet the RO should WAIT two years to apply for a new PR card. This is because their compliance with the RO is determined in processing the PR card application. But your RO has been determined based on H&C reasons. So it should be OK to proceed to apply for a new PR card soon.
In the meantime, while IN Canada, your CoPR and expired PR card, or at least the PR TD, are your best evidence of your status in Canada. This should suffice for some reasons. Might not be enough for some and you will need to wait to get the new PR card (which right now is a process that has, at the very best, fallen WAY, WAY behind due to Covid-19 protective measures). If you have your expired PR card, that should be good enough to qualify for health care coverage in at least the Province of Ontario (it recognizes expired PR cards for a period of several years past the expiry date). I do not know about other provinces. And in Ontario, the last I saw Ontario is waiving waiting periods (one among many Covid-19 related measures), so you might be able to qualify for OHIP (the Ontario Health Insurance Program) very soon after arrival rather than waiting (but you will need to visit the OHIP online information to verify this and how it works, for whom it works).
But to be clear, these are not easy times. As
@scylla suggested in the other part of the forum, you quite likely will need some substantial savings (or a Canadian based benefactor? family?) to support you for a significant period of time in Canada.
And back to bringing the children: I'd refer you back that other part of the forum for more coverage of questions related to getting temporary visas and making the sponsorship applications for the children. What I can offer is that the H&C decision on your PR TD application means that, ONCE IN Canada, you can being the sponsorship process without having to wait to have been in Canada two full years. Dependent, of course, on meeting all the other eligibility requirements for sponsoring dependents.