Question about Sponsor with child in another woman

[Avicon2016]

Hi, my husband (sponsor) had a child with his ex gf (we declare it as a mistake /one night stand with ex in Canada). In our application ", we mentioned that the sponsor signed a document before the child was born. We searched it online and thought it was the Acknowledgement of Paternity so we stated it in our application last june 2017. we just found out it wasnt. It's what they call Babymoon where the father can see the baby inside the womb. Then the visa office asked for the child's birth ceritificate and when the sponsor asked for it from the mother, she said his name is not on the childs birth certificate. How would it affect our application? We are trying to get the birth ceritificate from the mother. What if she refuses to provide it? We are given 30 days to provide the document.