I have had a relook at the information re "Elizabeth 2". Although you eventually ruled her out as being the unmarried sister of John Mann as she married Carling Shackleton in 1849, I am coming around to the view that she is the sister of John Mann but used "Mann" instead of "Shackleton" when she came out to NZ.
Could this have something to do with being a "Nominated single woman?"
Hi TPB
I've also been back over the info previously found for "Elizabeth 2" (Royalty, NOT ... but the one born c. 1828).

[And have been able to rule out other women of this same name. ]
She is with her husband CS > (and sometimes other of her family members) > in census returns 1851 to 1891. There are no apparent children of her union with Carling SHACKLETON.
Of course these census records at ten year intervals don't tell us "everything" ...and she may well have been the person (as an Aunt) who accompanied the MANN children to NZ. WHY

is the question ... and especially "why" when it comes to the young Robert MANN aged 7 (whose parents were still alive back in the old country) ? I'm sure he wouldn't just have "gone along for the ride".
* Maybe it was planned that (parents) John and Mary MANN would also come out to New Zealand at a later date ??
"Elizabeth 2" is listed as we know, "a single woman" with the occupation of "cook". In UK records she does not have an occupation - (shown as wife of an overseer - working in a mill or factory).
[Carling SHACKLETON's occupation was probably not one that was "needed" in New Zealand at that time ... but that would not preclude his coming to NZ, (in that era), as a colonial-nominated immigrant with his fare paid by somebody already resident in the Colony. And the same would apply to "Elizabeth 2" (too)

. ]
Added > Seemingly there were "regulations" for "nominated immigrants" - and probably each province had their own - but history tells us that on numerous occasion "rules" were broken (think persons tweaking their ages to gain subsidised passage / etc. etc. ).
<
:Unfortunately, if say this "Elizabeth 2" returned to England ... and in the company of a still-young, Robert MANN, before 1878, there are no shipping records/passenger lists covering that time frame.
... some more info to follow ... see next posts >
~ Lu