Just some other information:
1861:
Address: Brewster Ford Place, HolytownDavid Crow, m, head, 46, coal miner, b. Ireland
David Crow, m, son, 14, coal miner, b. Bothwell
Elizabeth Crow, f, daughter, 16, house keeper, b. Bothwell
Samuel Crow, m, 12, coal miner, b. Bothwell
Mary Boyle, f, grandmother, 61, -, b. Ireland
Women often reverted to their maiden name after being widowed and I feel the census entry here has been filled out by one of the children of David snr., making David snr. the actual son of Mary. This would add another child to John Crow and Mary Boyle.
It would be worth following him and trying to find a death for David to confirm parents. He should also appear on the 1841 and 1851 census in Scotland, so you may gain more information there too.
Good luck,
hume

PS. And just to confirm really, 1861 census for Jean Crow (now Cavanagh) shows she was living at the same place.
