Not much time today for family research but I did want to mention the following:
Received a very nice response today from the Department of Justice in the Cook Islands. It appears that they handle BDM requests so I should be able to get a death certificate for Alexander Barron.
Hmmm.....I do see the possible time line and geographical problems with Jean McMillan Barron. On the other hand, I keep coming back to her middle name and the way it is spelled. It seems Hugh may have used this spelling too, at least that's the way it was spelled by Wellington cemeteries. I was also thinking about whether an unborn child would, or should, be counted when registering for military service. Is it possible that an individual with two children would be less likely to be sent off to the front in Europe? That might be an incentive to put down two children instead of just one.
Regarding the non-appearance of Hugh in the NZ electoral rolls. I couldn't find anything either, nor could I find him in the Australian rolls.
I've been thinking that Hugh may have spent a good portion of his life in the Cook Islands. He was about 9 when his mother Susan died in 1924 and about 11 when his father Alexander married Vera in 1926. IF Hugh was the first born child, then the second child would have been even younger.
Alexander died in Rarotonga in 1932 when the two children were still teenagers. Assuming that they too were in Rarotonga they may well have stayed on with their step-mother. I know that Vera was still in Rarotonga in 1945 so maybe the 'kids' were too (Hugh would have been 30 then). Vera did return to the Wellington area (she is listed in the 1949 electoral rolls) but there is no mention whatsoever in her will or probate records of any children by Alexander and Susan.
Since there is nothing in the electoral rolls for Hugh, nor is there any pre-1956 marriage information for him, perhaps he did spend most of his life in Rarotonga (or at least not in NZ). Of course, the children could have been brought up by relatives of Alexander but then why is there no record of Hugh in the electoral rolls?
FYI, I am on the eastern seaboard of the US, about half way between New York and Philadelphia (and some 14,000+ km from New Zealand!)