My first thought is: it would help if the profiles of William Gannon and his children were sourced.
From a family member's tree, personal knowledge or unsourced family tree are not sources.
You need to provide actual sources such as birth, marriage, death or census records from the places where the family lived whether in Carlisle, Cumberland, England in the 1850s or from where the children moved to in New Bedford, Bristol, Massachusetts.
Have you looked at records that are available ?
There is a family tree for this family on Family Search,
https://www.familysearch.org/tree/person/details/GKMZ-BJS
It may not be accurate/correct.
It does not include any sources from Ireland.
It may not be possible to find records from Ireland for this family when they were living in Ireland.
There could be records perhaps death records or citizenship records for children or grandchildren of William in the United States that include a place of birth for William.