A legal question

I am applying for permanent residency by skilled workers program but I have a legal problem, and I wish to get an advice from your side.

I am married with a foreigner woman by Egyptian laws and we are living in Egypt for 4 years, but she returned to her country to give birth for our first baby (now he is 7 months old)

She refuses to apply with me for permanent residency in Canada, refused to supply me with her documents or the child’s documents.

The main problem is that she certified the birth of baby in her country as a lonely mother (because our marriage is not registered by her country’s laws) and she gave the baby intentionally her family name not my family name.

My family registered the baby at Egyptian authorities, acquired an Egyptian birth certificate contains the names of parents but place of birth is Egypt which is not true, And with different date of birth.

Now the baby has 2 different birth certificates from 2 different countries, with 2 different date of birth, 2 different place of birth and even with 2 different family names as following:

1-      Egyptian birth certificate with right names but wrong place of birth and date of birth

2-      Foreign birth certificate with right place of birth and date of birth but wrong family name

I tried to solve this conflict but this is a long and complex process and needs long time to modify.

My question now is:

What is right (or better)?

To provide the Egyptian birth certificate? Or to neglect it (as if it is not present)?

If I will put the Egyptian birth certificate, should I mention and clarify the problem? Or no?

What is the right action in my case?

Finally thank you for your help, I wish to get the right legal answer.