I've finally got a copy of the Intention to Marry, which doesn't shed much more light on things. It confirms her age at the time of her marriage, which is different to what was declared at her death, and tells us the occupations her and Thomas. It also gives us the streets they lived in at the time of their marriage.
Interestingly, in PapersPast, I have also found an inbound shipping passenger list, for 1874, showing that Mrs Neagle and family (5) arrived from Wairoa. i didn't find a matching outbound passenger list. At the same time (1870s), Thomas was on the electoral role because he owned two sections in Clive. I've also found reference to the Neagle children in the school prize giving articles in the local newspapers of the time.
Wairoa had a sawmill and a whaling station in the 1800s. Family "legend" has it that Annie's father was a sailor in the whaling industry, but there are also references to a Jackson involved with the sawmill.
Annie's death record describes her father as "Jackson (sailor)" and through other information we always believed he died in 1860, so why was she returning, with her children, from Wairoa in 1874?