To add to your most recent posting, I went to the library this afternoon and whilst there looked up the monumental inscription recorded on Andrew and Jane’s headstone. It was as follows
Sacred to the memory of ANDREW CUMMING of Bloomfield, native of Cummock, Ayrshire Scotland born October 1838 died 16 July 1918. Also his beloved wife JANE, died 22 October 1926 aged 85 and their daughters MINA died 17 November 1943 aged 75, MARION died 9 February 1947 aged 73, JANE died 2 December 1950 aged 79.
Clearly the stone was erected after 1950.
There was also a record of a William Cumming who died 23 May 1962 aged 88. He might also be related. Perhaps a son.
The history of the Hokitika Borough Council records that in its first election on 3 October 1866 an Andrew Cumming, a storekeeper was elected. It includes a photo montage of those elected including a heavily bearded Andrew. Difficult to guess his age but he certainly looks around 30. I wonder what his obituary might have said? This Andrew and yours might be one and the same person.
Stark as the maiden name of her mother fits easily within the normal British naming patterns and if Andrew had any say his parents names will be amongst their children as well.
Finally parents were often the official witnesses at weddings so it is possible that David Miller is her father.