I am NO expert. Anyone purporting to be an expert here is most likely NOT an expert either, or at the least should NOT be trusted to be an expert.
No one here can provide more expertise than a qualified licensed immigration lawyer. (Thus, if the expertise of a qualified lawyer is not good enough for you, you are NOT going to be satisfied with what anyone can provide here.)
You do not need a valid PR card to travel to your home country.
Of course traveling abroad without a valid PR card can be risky, and will typically require obtaining a PR Travel Document for the return to Canada. Depending on which visa office is involved in making the application for a PR TD, that can pose logistical issues, an uncertain or lengthy timeline, and depending on the facts it may involve some risk the visa office denies issuing a PR TD.
BUT nonetheless, a PR who is in compliance with PR Residency Obligations can travel abroad and then should be able to obtain a PR TD for the return trip to Canada.
Urgent PR Card Process:
In the meantime, the process for requesting urgent processing of a PR card application is clearly stated at the IRCC website, addressed in the same group of web pages where information about applying for a PR card is found. It is NOT complicated. It is, however, fairly easy to anticipate your situation might preclude urgent or expedited processing (PRs who have been outside Canada more than in Canada, during the previous five years, tend get bogged down in non-routine processing, and will typically not be given urgent processing, at least not until later in the process).
There is NO harm in making the request, and perhaps given the process you have already gone through in sponsoring your child, IRCC might indeed expedite the application and issue a new PR card on an urgent basis. The instructions are easy to find and should be fairly easy to follow.
Relevant IRCC information:
https://www.canada.ca/en/immigration-refugees-citizenship/services/new-immigrants/pr-card.html
https://www.canada.ca/en/immigration-refugees-citizenship/services/new-immigrants/pr-card/apply-renew-replace/urgent.html
https://www.canada.ca/en/immigration-refugees-citizenship/services/new-immigrants/pr-travel-document.html
Some Further Observations:
As already noted, no one here can provide more expertise than a qualified licensed immigration lawyer. It is NOT true that "all lawyers are thief's" or thieves. It is NOT true that "Lawyers just push to appeal because they make lot of money from it."
I am sorry you have had a bad experience with the lawyers you dealt with. With the usual exceptions, recognizing that not all lawyers are created equal or are equally skilled, generally lawyers can help a lot to make the best of the situation. They do not perform miracles. They cannot change the facts. They cannot change what the law requires. No more than a doctor can control a person's medical condition. But like doctors they can diagnose problems, prescribe the therapies or treatment most likely to help, and offer a prognosis. And lawyers can stand before a tribunal or authority as a representative of the client, employing their expertise and experience to better make the case . . . which, nonetheless, is limited to the facts of the case.
If you have read all decisions in immigration appeals for a three year span, you should be able to handle most of these transactions yourself. But if indeed you did this you should have readily recognized that the outcome of appeals is not a card game, coin toss, or any other game of chance, but is fact-based, criteria driven.
I personally do not know the percentage of outcomes in immigration appeals. I am personally acquainted with enough appeals to know that the vast majority are related to refugee or protected person applications, and NOT about the obligations of Permanent Residents. My strong sense is that more than ten percent of Residency Obligation related appeals are approved by the IAD, but almost exclusively for H&C reasons. Only a relatively cursory review of the facts in cases involving PRs, and the Residency Obligation, is necessary to recognize that in all but a very few cases the decision being appealed was CLEARLY VALID IN LAW.
Again, lawyers cannot change the facts. In the overwhelming majority of the cases, the determination that the PR was in breach of the PR RO, whether made by a Minister's Delegate (attendant PoE Report for example) or Visa Officer abroad (denying a PR TD application), is clearly CORRECT. Or, as the IAD states in the appeal, "valid in law." That is, as a matter of fact the PR was absent from Canada for more than 1095 days within the preceding five years (or since landing for PRs still within the first five years of their landing).
Thus, even if the IAD approves only 10% of PR RO appeals, that means many, many cases are won even though the PR was clearly in breach of the PR RO and thus inadmissible. (Noting, again, however, even though I am not certain my sense is that more than 10% are approved. Also noting, however, that not all those approved involve a lawyer on behalf of the PR. IAD appeals are often prosecuted without a lawyer representing the PR. Foolish in my view, but the procedure itself is not that complicated, not at all as difficult as trying to take a Mandamus action to a Federal Court for example.)
Many if not a majority of appeals in PR RO cases are essentially acts of desperation. The PR knows he or she has breached the PR RO. Knows he or she is inadmissible and that an order terminating PR status is VALID in LAW. The appeal is their only chance to save their status. They appeal hoping that H&C reasons are sufficient to persuade the tribunal (the IAD panel) they deserve a chance to keep their status. Most of these cases are a long shot. A very long shot. Even the best H&C cases can be and usually are tricky, with only a few exceptions (minors removed by parents tend to have a strong case so long as they timely make the effort to return to Canada after emancipation). Lawyers tend to be far better identifying and arguing H&C reasons than individual PRs. But again they cannot change the facts or law. And the outcome of these cases is largely dictated by the facts and the law.
There are good reasons, after all, why experienced participants here emphasize, again and again, that notwithstanding how the 2/5 rule will allow a PR to be abroad for virtually three years, staying abroad anywhere near so long is risky and asking for problems.
In the meantime, anyone who has gotten themselves into a jam regarding the PR RO can usually benefit from the advice and assistance of a qualified lawyer. It is expensive. I agree that it tends to cost more than it should. And one still needs to be their own personal best advocate, just like when dealing with doctors. And there are no miracles in a lawyer's brief case. BUT for those who can afford it, lawyers can improve the odds.
so yes, By God's grace, everything worked out. The sponsorship process was normal, submitted all the required docs, nothing more n nothing less and just let it take its own course.