Hi,
May I explain why she is not listed on her mother's dc. I will probably be a tad long winded in the explanation.
Firstly, in NSW, it is the funeral director who arranges for the information to be gathered together, and it is the funeral director who forwards the paperwork to the NSW BDM. They do this in a formal way.
On the historic certificates you can see the way things were done in that era, in the particular jurisdiction that governs those documents. In Australia each of our states and territories have their own legislative authority to set their own laws, regulations and practices. So my answers relate to NSW BDM ways, and the historic death certificates.
So you see, the funeral director is responsible for the funeral service, and for the paperwork. So when the funeral director is meeting with the family, they organise together the order of service, the suitable date, the eulogy, the family members will each help each other with their own grief, and help with the paperwork, and one family member usually becomes the 'informant' - the person who provides answers to questions about the deceased's family members. One of the questions that the informant was required to answer relates to children of the marriage. It was actually a difficult question in those times. Thinking about it ... The question asked was not "how many children", nor was it "what are the names and ages of the children"; in fact it was an intrusive question.
So the question asked was 'what are the names and ages of the children of the marriage'. So if the person had not ever formally married, but had several children, in a strict sense, none of those children were eligible to be named as children of the marriage. In the same way, if a child was born prior to a marriage, it was possible that the funeral director in preparing the paperwork to forward to the NSW BDM did not include a child born before the deceased had become a married woman.
So, it depended on how the funeral director asked the question, and who the funeral director actually asked, as to how accurate/reliable the information recorded on the death registration became. So, for example, when I look at the death registration for one particular family member of mine, I can see that there's an entire marriage and three children who are not included in the information on that dc. To me, it is simply that the informant did not provide the information (either did not know, or did not know how to tell the funeral director). Perhaps the informant was distracted, or more likely was grieving and needed more time to give all the details.
I hope this long winded explanation helps. The NSW BDM system now allows for the deceased's Children to be included, regardless of whether the deceased was married or not.
JM