Nellie was baptised Clements and her birth cert is also Clements, her father was born/baptised Smith and later added his mothers maiden name of Clements, however none of his children were baptised with the name Smith.
I have the marriage cert of her marriage to John Paterson which is where I found she was a widow and previously married to a Mr Barker.
I knew her when I was a child, she died in 1972 in Nottinghamshire and is buried in the family grave yard ( John is buried there too in 1959, so I never knew him)
On the 1911 census she is 21yrs old single and living/working for a family in Bullwell Nottinghamshire, then in 1933 she is marrying John Paterson in Glasgow aged 41yrs and a widow ( as he was as well)
So her first marriage was between 1911 and 1933, no idea where.
I have John Paterson up to the 1901, can't find him or his parents/siblings on the Scottish 1911 on marriage( 30 May 1933) he was living in Shore Cottage Portencross Ayreshire
The only maybe marriage I can find
Nellie Cleminson 4Q 1919 Tynemouth 10b 650/56 Harry B Barker but it is difficult without census and the surname is different and with lots of Nellie Cleminson's on the birth index, so I don't think it is her