Looking for information on Mary Sweeney, married to William Shannon with daughters Margaret, Bridget and son Bill

At the paid site rootsireland, I found baptisms for the following children of William and Mary. There were three sons: John, Wm., and Henry.

                              Shannon              Margaret My      1876      Co. Galway        

                              Shannon              Elizabeth              1877      Co. Galway        

                              Shannon              Bridget  1878      Co. Galway        

                              Shannon             John      1880      Co. Galway        

                              Shannon              Teresa   1881      Co. Galway        

                              Shannon              Maria Agnes       1882      Co. Galway        

                              Shannon             William Jos         1884      Co. Galway        

                              Shannon              Catherine            1886      Co. Galway        

                              Shannon             Henry    1887      Co. Galway        

                              Shannon              Clara      1890      Co. Galway        

                              Shannon              Emily     1892      Co. Galway        

                              Shannon              Rachael 1892      Co. Galway        

                              Shannon              Harriet  1894      Co. Galway        

Here's the family in the 1901 Irish census:

Residents of a house 5 in Athenry Road (Loughrea Town, Galway)

Surname              Forename            Age        Sex         Relation to head               Religion               Birthplace               Occupation         Literacy Irish Language    Marital Status     Specified Illnesses

Shannon              Mary      50           Female  Head of Family   Roman Catholic Co Galway           General Labourer              Read and write   Irish and English Widow  -

Shannon              Henry    14           Male      Son        Roman Catholic Co Galway           Scholar  Read and write      -              Not Married        -

Shannon              William 16           Male      Son        Roman Catholic Co Galway           Scholar  Read and write      -              Not Married        -

Shannon              Rachel   [8]          Female  Daughter             Roman Catholic Co Galway           Scholar               Read     

http://www.census.nationalarchives.ie/pages/1901/Galway/Loughrea_Town/A…

From the 1911 Irish census:

Residents of a house 4 in Ballinlawless (Kilteskill, Galway)

Surname              Forename            Age        Sex         Relation to head               Religion Birthplace               Occupation         Literacy Irish Language    Marital Status     Specified Illnesses            Years Married Children Born      Children Living

Shannon              Mary      62           Female  Head of Family   Roman Catholic Co Galway           -               Read and write   -              Widow  -              -              -              -

Shannon              Henery  30           Male      Son        Roman Catholic Co Galway           Farmer  Read and write      -              Single    -              -              -              -

Shannon              Mary      28           Female  Daughter             Roman Catholic Co Galway           -               Read and write   -              Single    -              -              -              -

Shannon              William 26           Male      Son        Roman Catholic Co Galway           Farmer Son               Read and write   -              Single    -              -              -              -

http://www.census.nationalarchives.ie/pages/1911/Galway/Kilteskill/Ball…

Since you are looking for family in Ireland, perhaps contact the Loughrea FB group at

https://www.facebook.com/search/top?q=loughrea

Good luck.