I also concur in the observations offered above.
And I especially concur in the suggestion to at least consult with a qualified legal professional, a licensed Canadian immigration lawyer.
A lawyer can better answer your questions, from explaining the situation you are in, to offering what potential course of action you can take.
That is, it mostly comes down to seeing a lawyer about this, or stay in Canada until you are issued new PR cards.
That said (the long version):
That said, my sense is you want assurance you can leave Canada without jeopardizing your PR status. There are no guarantees in close cases. And of course the closer a case it is, the less predictable it is, the greater the risk.
Your questions acknowledge you recognize there are risks, and others have illuminated some of the parameters of those risks, and have emphasized they are substantial.
What is at stake is status to return to Canada to live. You could lose that. You could have your PR status taken away. And yes, this makes the decision-making very difficult in the circumstances you have gotten yourselves into.
The lowest risk in traveling abroad would be if you are delivered the new PR cards in time to travel. A lawyer may, possibly, help you accelerate the process to be delivered new PR cards. That is probably your best chance of being able to travel abroad before February without seriously risking your PR status. (Probably close to already being too late to travel by Christmas.)
And you can otherwise continue to contact CIC (see suggestions posted above by eileenf), your MP, and so on, also in an effort to get CIC to make its determination, which should be in your favour and should result in the delivery of new PR cards. And hope you get them in time to make the trip.
In the meantime, it appears that in what you submitted to CIC you may have mingled proof of urgency (reason for travel) and/or H&C considerations, with proof of compliance with the PR Residency Obligation. This is the sort of thing a lawyer would be particularly helpful in sorting out.
While proof of planned travel is necessary to obtain urgent processing, proof of the travel plan itself is sufficient to meet this. Once CIC did not deliver the PR cards in August, the question was not really about how urgently there is a need to travel but whether you (and your wife and children) were in compliance with the PR Residency Obligation.
Some observations about the risk of a negative decision, particularly as to the risk of being denied a PR Travel Document if you go abroad without a new PR card:
Obviously CIC has some concerns about you and your family meeting the PR residency obligation. While it may not be clear why CIC has those concerns, you know that CIC does. They gave you RQ. That is what that is about.
It may sound like a tautology, but once CIC questions the facts (such as once CIC decided to do a more thorough examination of compliance with the Residency Obligation), the facts are in question.
In other words, CIC is at the least questioning your account of how much time you (or your wife, or daughters) have actually spent in Canada.
That means, for example, that even though you say you and your spouse and your daughters met the PR RO, (918 days and 771 days respectively present in Canada within the five years that count), CIC is questioning that.
The burden of proof is on you.
All of you spent most of your time outside Canada, thus for any time period open to any doubt, from CIC's perspective, from a total stranger's perspective, reason leans toward the inference you were probably outside Canada during that time . . . because, again, you were mostly outside Canada, and where a PR was most of the time supports the inference that is where the PR was during any time not proven otherwise.
But as was said to you at the CIC office, your wife in particular cut it close. Add to that any other cause for questions, such as about reported address, that is a recipe for CIC to indeed have concerns.
What probably really matters most at this point is how well you documented actual presence in Canada. Documenting the travel dates is important, but not sufficient.
A lawyer may be able to go over what you submitted and offer an opinion about how well you documented your presence in Canada, for each of you. If your response to the RQ did well-document your presence in Canada, well enough to show compliance with the PR RO, the risk of being denied a PR TD during a brief trip abroad goes down. The risk of being issued a Removal Order at the POE upon attempting to return via the U.S. goes down. That is, while a lawyer cannot give you any guarantees, a lawyer may be able to assure you that your risks are relatively low.
Or, the lawyer may be able to look at what you submitted and conclude that the risks are indeed high.
If a lawyer opines that the risks are high, and you do not obtain new PR cards in time for your travel, while the decision will be very difficult to make, what is at stake in making the decision is fairly clear: travel to be with family at the risk of no longer being able to live in Canada, or stay in Canada to preserve PR status.
And I especially concur in the suggestion to at least consult with a qualified legal professional, a licensed Canadian immigration lawyer.
A lawyer can better answer your questions, from explaining the situation you are in, to offering what potential course of action you can take.
That is, it mostly comes down to seeing a lawyer about this, or stay in Canada until you are issued new PR cards.
That said (the long version):
That said, my sense is you want assurance you can leave Canada without jeopardizing your PR status. There are no guarantees in close cases. And of course the closer a case it is, the less predictable it is, the greater the risk.
Your questions acknowledge you recognize there are risks, and others have illuminated some of the parameters of those risks, and have emphasized they are substantial.
What is at stake is status to return to Canada to live. You could lose that. You could have your PR status taken away. And yes, this makes the decision-making very difficult in the circumstances you have gotten yourselves into.
The lowest risk in traveling abroad would be if you are delivered the new PR cards in time to travel. A lawyer may, possibly, help you accelerate the process to be delivered new PR cards. That is probably your best chance of being able to travel abroad before February without seriously risking your PR status. (Probably close to already being too late to travel by Christmas.)
And you can otherwise continue to contact CIC (see suggestions posted above by eileenf), your MP, and so on, also in an effort to get CIC to make its determination, which should be in your favour and should result in the delivery of new PR cards. And hope you get them in time to make the trip.
In the meantime, it appears that in what you submitted to CIC you may have mingled proof of urgency (reason for travel) and/or H&C considerations, with proof of compliance with the PR Residency Obligation. This is the sort of thing a lawyer would be particularly helpful in sorting out.
While proof of planned travel is necessary to obtain urgent processing, proof of the travel plan itself is sufficient to meet this. Once CIC did not deliver the PR cards in August, the question was not really about how urgently there is a need to travel but whether you (and your wife and children) were in compliance with the PR Residency Obligation.
Some observations about the risk of a negative decision, particularly as to the risk of being denied a PR Travel Document if you go abroad without a new PR card:
Obviously CIC has some concerns about you and your family meeting the PR residency obligation. While it may not be clear why CIC has those concerns, you know that CIC does. They gave you RQ. That is what that is about.
It may sound like a tautology, but once CIC questions the facts (such as once CIC decided to do a more thorough examination of compliance with the Residency Obligation), the facts are in question.
In other words, CIC is at the least questioning your account of how much time you (or your wife, or daughters) have actually spent in Canada.
That means, for example, that even though you say you and your spouse and your daughters met the PR RO, (918 days and 771 days respectively present in Canada within the five years that count), CIC is questioning that.
The burden of proof is on you.
All of you spent most of your time outside Canada, thus for any time period open to any doubt, from CIC's perspective, from a total stranger's perspective, reason leans toward the inference you were probably outside Canada during that time . . . because, again, you were mostly outside Canada, and where a PR was most of the time supports the inference that is where the PR was during any time not proven otherwise.
But as was said to you at the CIC office, your wife in particular cut it close. Add to that any other cause for questions, such as about reported address, that is a recipe for CIC to indeed have concerns.
What probably really matters most at this point is how well you documented actual presence in Canada. Documenting the travel dates is important, but not sufficient.
A lawyer may be able to go over what you submitted and offer an opinion about how well you documented your presence in Canada, for each of you. If your response to the RQ did well-document your presence in Canada, well enough to show compliance with the PR RO, the risk of being denied a PR TD during a brief trip abroad goes down. The risk of being issued a Removal Order at the POE upon attempting to return via the U.S. goes down. That is, while a lawyer cannot give you any guarantees, a lawyer may be able to assure you that your risks are relatively low.
Or, the lawyer may be able to look at what you submitted and conclude that the risks are indeed high.
If a lawyer opines that the risks are high, and you do not obtain new PR cards in time for your travel, while the decision will be very difficult to make, what is at stake in making the decision is fairly clear: travel to be with family at the risk of no longer being able to live in Canada, or stay in Canada to preserve PR status.