Ar_fabrics, please let us know what you find out about whether you can apply for your children abroad. I highly recommend contacting a settlement agency or lawyer to clarify this.
And I (again) highly recommend applying for your child who is a resident. The risk for delay in your own application is extremely slight. From what I see, many seem to consider it to be the wife's responsibility to ensure the citizenship of the children by making the family application, but it's really worthwhile to ensure that you provide your children the protection of citizenship sooner rather than later. What if your wife doesn't apply? What if your wife doesn't return to Canada? What if your children lose their PR status?
Here are some of the protections that citizenship provides over PR for your resident child: God forbid: A child turns 18 gets in legal trouble. Yes, none of our children would never do such a thing, but young people make mistakes. It happens. The question is whether the child will be able to triumph over such a challenge or will end up deported. A child uses a fake ID to get into a bar. A child is mixed up with the wrong friends and is in the car when there's a hit and run or drunk driving or someone steals something or (God forbid) hurts someone. If the charge is serious enough, the child could lose their PR status and be deported. And then they are delayed or barred from re-sponsorship due to criminality. Citizenship would have avoided this problem.
Another reason: A child decides to study abroad and gets a great opportunity to stay for an extra year. Do field work. Research with a renowned professor. Learn another language. This puts them in violation of their residency obligation and they lose their PR the next time they try to return to Canada. Applying sooner, rather than later, for citizenship could have avoided this.
Another reason: Your child's classmates go on a study trip to the US, but your child's passport is from a country that doesn't have good relations with the US and the child can't get the visitor visa. Not a huge deal, but a lost opportunity.
The reasons not to apply for your children are that it *might* make things easier for you personally. The reasons to apply for your children are a lot more serious. Giving your child the protection of Canadian citizenship is a huge thing. It's real. On the pros vs. cons list, providing protection for ones children (as a parent who's clearly concerned about their children and wants the best for them) should rank pretty high, especially when the risk or downside to one's own case is so slight.