Susan,
In my opinion Mary Rainey was having a little fun when she put “lady’s nurse” down for her mother’s occupation. You can see that in 1911 Mary had 6 children under 10. I think her mother was helping look after them, and consequently Mary had her tongue firmly in her cheek when she completed the form. Mary herself was the “lady” referred to.
In the 1901 census her mother was described as an “annuitant” ie she had income from an annuity or pension (perhaps triggered when her husband died). So she didn’t need to work professionally I suspect, and just helped Mary nurse and rear her children.
The Steel(e) family don’t appear to have any obvious ancestral connection with Ireland. Mary and her mother were born in Greenock so presumably that area would be the place to look for her relatives.
I wondered if this probate abstract might relate to Robert Rainey senior:
Rainey Robert of Randalstown county Antrim retired engineer died 7 May 1924 Administration Belfast 16 June to Mary Ann Rainey widow. Effects £388 16s. 6d.
Above was aged 72, so born c 1852. That in turn seems to lead to this family:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Woodvale_Ward/Eastland_Street/986431/
http://www.census.nationalarchives.ie/pages/1911/Antrim/Woodvale/Ashmor…
Rainey is a very common name in Randalstown. Here’s son Francis’s birth in Ballygrooby, Randalstown in 1880. So the above family has some connection with Randalstown. Ballygrooby is on the outskirts of Randalstown as you approach from Belfast.
https://civilrecords.irishgenealogy.ie/churchrecords/images/cert_amends/cert_1880/2058051a.pdf
Now the main snag with the above family is that the mother’s maiden name is Leech not Johnston. Can’t explain that but a number of trees on Ancestry appear to think it’s the same woman. Not sure what their evidence is. Here’s the Rainey-Leech marriage in 1871:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1871/11350/8166485.pdf
