** I've also been told that because we've applied for her citizenship certificate she may be let in as a presumptive citizen. No idea what that means though.
Since I wrote (I think) this presumptive citizen term - a strong warning that, you know, don't take legal advice from a random guy on the internet, and I doubt this term is the proper legal term, I just used it in general common English language sense.
My point overall is that seems very unlikely that CBSA would not let your citizen-husband's daughter in the country since you have evidence applied for citizenship, and about as unlikely they would attempt to claim her time in Canada is limited to usual visitor time limits. (With the background of Canadian citizenship law that she was born a citizen or with a claim to citizenship - but no final determination/confirmation of that ... which is all I meant by presumptive, and it's my term, I don't know if that is correct legal term).
What Canadians who travel by air (eg from rest of world) for children in this situation generally need to do is apply for a passport at same time as submitting the citizenship application. And they're granted 'temporary' passports (not sure of the term here either) - usually good for two years? - to cover the time in which the finalization of citizenship should be completed. Similarly, presumptive - in the sense that they wouldn't issue it if the claim to citizenship wasn't clear and pretty obvious, and it's just pending the final confirmation. (And I assume that
hypothetically the claim to citizenship could be denied...). But usually eventually the citizenship is confirmed and a new passport applied for/issued.
So it would by far (I think) be preferable to apply for a passport for your daughter on an urgent basis, I just don't know how that works for your timing. And
probably it won't make much difference because experience usually seems to be that at the border the CBSA agents don't deny entrance to the children in cases like yours.
And a side note: I don't know how this will work for your child for other important stuff in the short term - notably health care. And I won't even attempt to guess at that because depends on province, etc. I'm pretty sure that all provinces would accept these 'temporary' passports issued as evidence of citizenship - and no idea how they would handle it without them - and then there are waiting periods (currently waived in some provinces), etc. So may still be a good idea to apply for passport for the child.