Can I make a suggestion?
There has been lots of guesses and errors in the information on the other posts. You were not sure of details likely at that time. Can you do a quick summary of what has been confirmed so far?
For example, your grandmother's name looks to be Mary not Bridget.
Now that you have the original marriage for them in Dublin in 1940, I see one of the witnesses is a Joseph Brady. To fit with the story that father Joseph abandoned them as children, could this be one of his two brothers?
I can't make out the occupation for Joseph, father

Monica