Hi
I had a quick look on IGI for Cecilia REID marrying sometime in the 1860s.
I could only find 3
1. CECILIA REID -
Female Marriage: 03 SEP 1861 Tradeston, Glasgow, Lanark, Scotland
2. CECILIA REID -
Female Marriage: 03 MAR 1862 Bridgeton, Glasgow, Lanark, Scotland
3. CECILIA REID -
Female Marriage: 21 NOV 1862 Abercorn, West Lothian, Scotland
Taking Abercorn as a likely candidate as it is relatively near Dalkeith - her marriage was to Robert Orrack 21 Nov 1862 Batch No M116611
I looked for Births in Abercorn after that time frame but found none and there are too many Horroks/Orrocks/Orracks to go through. After 1000 and I was still only as far as the Alices I gave up.
The only Cecilia Keddie I found was her first marriage!
Have you tried to find Cecilia on scotlandspeople.gov.uk ? It looks as though she died after the introduction of Statutory Records in 1855.
Since it is a pay site you might have to use some credits to eliminate some names from your enquiries buit her death certificate entry would give you the name of her second husband and probably John Reid's as well. If known, her parents would be listed too although I approach the 'parent names' entries with some scepticism as many of my 'finds' have got it wrong, particularly if they were dead a long time before her second marriage.
The 1861 census might help to locate children by her first husband if they were still at home.
good luck
Russell