I have Currans from Ramelton (Rathmelton) so was interested to read this post. I would be interested to know if you ever found out who Catherine's parents were.
Uddingston would not have been part of Glasgow but a village in the parish of Bothwell, Lanarkshire. (I live about 5 miles from there).
According to the 1881 census they lived at Udston, which is part of the town and parish of Hamilton, Lanarkshire.
The census reference is 1881 - 647 - 23 - 12. The address was 36 Udston Single Rows. (May have been 36 Single Row, Udston, Hamilton).
Francis and Catherine are there with 6 children.
All have the surname Newlands -
FRANCIS, head of house, married, aged 32, coal miner, born Oakley, county of Fife.
CATHERINE, wife, married, aged 27, born Ireland.
JAMES, son, aged 12, scholar, born Glasgow.
WILLIAM, son, aged 8, scholar, born Glasgow.
MATTHEW, son, aged 6, born Hamilton.
MARY JANE, daughter, aged 5, born Hamilton.
FRANCIS, son, aged 2, born Blantyre.
MAGGIE, aged 8 monnths, born Hamilton.
Glasgow, Hamilton and Blantyre are all in Lanarkshire.
Lodger.