According to that we would need to show a) The child's mother is a PR and b) the relationship between child and mother.
b) is not a problem, just a birth certificate I guess.
a) is more problematic as the mother does not have a current PR card. She has an expired card, and a copy of her COPR. Question is will the airline staff accept those as proof of the mothers PR, you know what they are like some times!