VEC/TRC in de facto marriage. Any one done before?

Hello!

My Vietnamese GF and I have recently got a cute son here in Saigon. We haven't got married yet and would probably not to do so for the next 3-4 years since we decide to live together first before pledging anything.

I am currently staying here with 3 months travel visa but would like to apply 3 or 5 years of VEC. It seems that I am qualifying to apply it since I am a "parents" of my Vietnamese son even though my GF and I have not officially got married.  ( In my son's birth certificate and in my home country's family book, I am registered already as a father of my son). I am now preparing to apply VEC or TRC based on this family relationship.

My issue here is if my 3 months-old-son can play a role as my sponsor to obtain 3/5 years of VEC or TRC. It looks like that people got such qualifications based on their marital relationship but not on a parents-children one especially when an applicant is a parent but not a children.

Would be very much appreciated if you share your experience.
Thank you ahead! 

Edward