Please don't keep re-quoting so many replies as it gets more and more confusing to read.
The 1923 birth is [presumably] eldest child of William Lines and Hannah Heyburn. They married on 10 Mar.1923 and daughter Florence was born 23 Nov.1923 (Newtownards registration district).
I asked if you were aware of this child since it would have provided yet more evidence that we have found the correct Heyburn family.
I have just checked for a death in Northern Ireland (1923-1940) but there was none for Florence. Perhaps you'll be able to find information about her in English records.
Before I post details about the Heyburn family, I did find a possible death for Hannah's mother, Martha Heyburn, in Scotland. I say possible because the name and age fit. However, I have not viewed the certificate. IF Martha died in Scotland the informant may not have known much about her so the details on the death registration may not be able to confirm it is Hannah's mother. It would probably be worth first checking to see if she died in England in case she went to live near Hannah.
HEYBURN MARTHA 69 F 1939 595 / 80 Irvine