What we are finding doesn't entirely match with the information you have so far. We have this family in 1911 census where husband William is tinsmith, wife is Mary, and there are sons John & William-www.census.nationalarchives.ie/pages/1911/Cork/Cork_No__3_Urban/Old_Youghal_Road/386537Son James born 1911- LINK (mother Dillon)The John Driscoll birth 1907 is John my grandfathers brother born before our William and Mary got married in 1908 A John Driscoll born 1907 to unmarried Mary Driscoll- LINKMarriage of William Driscoll & Mary Dillon 1904-https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1904/10194/5709608.pdf
Driscoll/Dillon marriage and birth of son James posted in reply #14Unless OP can turn up marriage for William Driscoll to Mary Driscoll then I suspect that they weren't actually married.
The John Driscoll birth 1907 is John my grandfathers brother born before our William and Mary got married in 1908