Since she is still moving back and forth, I would consider that she is not exclusively living outside of Canada, at least not yet, and therefore she should not need to prove that you intend to live there. She can give her address as whatever address she stays at when she is there, parents or otherwise.
The baby will be a Canadian citizen but that will not matter for your application for PR.
You can find the forms at
http://www.cic.gc.ca/english/information/applications/fc.asp The guide is at
http://www.cic.gc.ca/english/pdf/kits/guides/3900E.pdf