Give up.
Get Ann and Alexander's marriage certificate. Look - witnesses! James Smith scribble. And Margaret Smith scribble. Buggar.
Show certificates around at reunion. Think the word is Vial, but what sort of a name is that? Or occupation. Vial? I've heard that name says Auntie Mavis. Hmmm. Vial - unusual name. Better than Smith. And the woman is Margaret Vial - same name as Annie's mother. Hmm. Connection?
Spend a day in the LDS Family History Centre at Templeton. Vial is an unusual name, and what's more, I can track the births, deaths and marriages right through the generations. Children named Lawrence. This is getting better and better. Spend some time at the National Library in Wellington - Intention to Marry filed for James Smith VIAL and Margaret SMITH. Same last name as Ann. Margaret arrived in Otago about five months ago. It fits!
Finally, take a risk and order the death entry of Margaret. Parents: Lawrence SMITH (Painter). Margaret EWING. Bingo! I can't believe that I proved the family story.
It doesn't end there... recently I dialled the phone number of a certain VIAL in Christchurch. He was amazed at the connection, and informed me that GORDON was one of his middle names. He had never known why.