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There's an interesting family boarding with the Phinns in the 1881 Census in Dundee:
93 Ann Street, Dundee
James Phinn, 40, gen labourer, b. Ireland
(and family)
Mary Ann Burns, boarder, unmar, 30, Mill Worker (Jute) , b. Ireland
Thomas Burns, boarder, 7, b. Dundee
Margaret Burns, 5, b. Dundee
There were 4 or 5 birth registrations for a Margaret so I looked for a Thomas:
March 14 1874
Thoams Burns (illegitimate)
b. 11 William Street, King Street, Dundee.
Mother - Mary Ann Burns, Jute Preparer
I don't know if this is your Mary Ann but it's worth keeping on the back burner as this seems to fit with Ruskie's Reply #4
Gadget