As a PR, you can not sponsor when you yourself are living outside Canada. This is a headache for all PR's from visa exempt countries that have babies outside Canada. You can not sponsor from outside so you want to take the baby with you to Canada and sponsor from inside. Then you apply for a TRV for the baby, may be denied because your intention is for the baby to live in Canada, not stay temporarily. Maybe you can get a TRP for the baby, a special permit for people who are generally inadmissible for a TRV but have good reason to be in Canada anyway. If you can't get that either, your only choice is to leave the family behind and go to Canada to sponsor by yourself. If you and your family are tight on the residency requirements, that could mean that your wife and other child will have lost their PR by the time you are ready to go back. That is why it is a headache. I do not know what your council is planning to do. There is no way for a PR to sponsor the baby while not living in Canada. Your council can try to fake the paperwork but when immigration finds out you are not in Canada, they will deny.
If you want to finish a work contract where you are, you could send your wife to Canada earlier with the older child and you keep the baby with you. Your wife could sponsor the baby and hopefully you would have it through before you want to go yourself. You can also ask the embassy where you are if it is possible to get a TRV or TRP for the baby.