In the 1861 census Bridget Sharkey was 43 so this puts her birth around 1818.
A Brigittam Cahalan was born in 1818 in Tibohine to Jacobi Cahalan and Margarittae Carty.
Luke Sharkey (Bridget's first child) was born around 1848 in Ireland.
Brigida Conahgan married Joannes Sharkey on 28 January 1848 in Ireland.
That marriage took place in Donaghmore, Derry. February 28th 1848
It is difficult to read but note the marriage above also.
You have Francis Gallagher and Catherine Conaghan.
John Sharkey and Bridget Conaghan are witnesses to that marriage and vice versa.
There is mention of ‘Glasgow’ for Catherine but not sure what it means. Perhaps someone can help.
https://registers.nli.ie/registers/vtls000633031#page/98/mode/1upIn 1851 2308/377/7
Luke is 4 yrs old - so a birth 1846/7.
In 1861 he is 14 yrs old but then his age does vary.
I have just looked for baptisms in Donaghmore and there is this:
Catherine Sharkey 3rd May 1851 to John and Bridget Conaghan.
https://registers.nli.ie/registers/vtls000633031#page/40/mode/1upI would say that the marriage you have is the wrong couple. You have your family in Bradford in 1851.