Hello again Judy!
Take a look at this 1901 census reocrd which has a 70 year old Bridget with a daughter in law Catherine and a grandson John. The husband of Catherine was not in the household when the census was taken. They lived in Kiltogorra townland Cong civil parish http://www.census.nationalarchives.ie/pages/1901/Mayo/Cong/Kiltogorra/1577348/
Here is the civil birth record for John Phillips in 1897 (fifth record on page) https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1897/02124/1807294.pdf
The father is shown as Patrick Phillips. Likely young John was named after his paternal grandfather.
I know that you have Bridget Conneely born in 1845 but I believe this is your family.
Bridget died in 1905 (fourth record on page) and she was shown as 60 https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1905/05599/4573897.pdf which ties back to 1845.
Here is the 1911 census for Kate Phillips and a four year old daughter Bridget http://www.census.nationalarchives.ie/pages/1911/Mayo/Cong/Kiltogorra/705067/ Once again Patrick was not in the household. John the son was deceased.
I found his death record also in 1905. He died from burns (third record on page) https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1905/05591/4571059.pdf