What was David's occupation according to Mary's marriage certificate? And who were the witnesses?
The only slight chink of light might be a David Consterdine, aged 10, born Scotland, in the 1861 census in Nottingham. In 1851 he's with parents Joseph and Ann Consterdine in Mansfield.
Could Joseph and Mary's father David possibly be connected in some way?
Joseph's age in 1851 is recorded as 27 and he is an engineer, born Clown, Derbyshire. There's a baptism of Joseph, son of David and Elizabeth Consterdine, in Clowne, Derbyshire, on 22 November 1823.
David Consterdine, 61, born Clowne, is in the census in 1861 in Nottingham with a wife and two stepchildren aged 20 and 21. In 1851 he's a widower, at Point Court, Nottingham. In 1841, in Point Court, is D... Constandine, 42, not born in county, with Elizabeth, 41 and Joseph, Abraham, Isaac and Selina. The D... is indexed as Daniel, and I can see that it looks like that, but it could also be deciphered as David. He is described as an engineer.
Speculation. Is it possible that Mary's father David was Joseph's brother, and that both brothers went to work in Scotland for a couple of years, perhaps on a contract, taking their wives, and both having a child born while they were there? As they were clearly English, such children could have been baptised in an Episcopal church, the records of which are not in the care of the National Records of Scotland and therefore not on Scotland's People?