My error in concluding the death cert mentions Albert living with her. That information came from a report in the Christchurch Star which states he was living with Mrs Williams.
https://paperspast.natlib.govt.nz/newspapers/TS18911124.2.37Star (Christchurch), Issue 7138, 24 November 1891, Page 4
With regard to 15 year old Alice Howarth, I have placed her to one side as the eleven year gap between arriving at Port Chalmers and giving birth to Annie in 1885 doesn't make a lot of sense. I obtained a death certificate for a Margaret Alice HOWARTH b. October 1859 Elton, Bury Lancs. Parents James & Lydia (Nuttall). This seemed to have potential until 1864 when Lydia died aged 37. In the 1871 census return it appears James remarried Ann however, on Lancashire BMD, there are both Ann and Mary Ann but when checking them against the birth of the youngest girl, Selina, none of the mother's surnames match with those on the GRO UK. I've been told the Lancashire records are variable. As I tracked the family through the census returns it became clear James died sometime between 1871 and 1881 - I haven't finished checking through those details, but it did look as though Margaret A was still living in the UK in 1891 so she isn't the one, although again, I will put her in my to be reviewed pile which is growing larger each day
I'm still to receive the birth and death info on Annie and continue to work my way through the Margaret Alice (Howarth, Howorth and Haworth) birth registrations. I have applied for a birth certificate for Margaret Alice Haworth b in the M quarter of 1859, Rossendale, Preston, mother's maiden name Farnworth.
According to the Lancashire records there are current no records for an Alice Margaret Howorth, Haworth or Howarth, born between 1857 and 1862. There is only one Alice Margaret recorded on the GRO UK, J Quarter of 1860, mother's maiden name Orrell, so one more name to add to the list.