I am wondering now if there was just some confusion in the family, as the only firm record seems to be on her death certificate and that information tends to be the least accurate (as depending when they went to Australia, . Her son even has the Hope surname as a middle name, and she fits in neatly between George Henry (December 1875) and William Frederick C (Dec quarter 1878). It's not as if there is some inconsistency that suggests she might not be Janes' - e.g. if she was the youngest by some way, if her birth was three months after that of another child.
we know that Norman grandmother registered Eveline birth
The mother of Job Shackleton? A person present at the birth could register it, and older female relatives often acted as midwives for home births. By itself this is not unusual. The address of birth, if this wasn't the usual family address, could be a hint.
We do not appear to have any census records showing Harriet in the household (not with Job and his parents in 1871, not with Job in 1881, not with Job's parents in 1881, there are no possibles for her that I can see in Sunderland in 1871 and 1881 at all).
Remember that family stories are like a game of Telephone. There presumably was a Harriet Lawson involved in the family somewhere, perhaps a relative who was close to Eveline, because names generally do not appear out of thin air. However, as Norman was only 5 when Jane died, and then the family moved across the world a couple years later, he presumably had few memories of his grandmother. And we have no way of knowing whether, in fact, after marriage in 1901 if Eveline was in much contact with her family (for example, if they didn't approve of Robert).
