The referenced Michael Brady was indeed the son of Eoin (Owen) and Catherine Brady.
I have that Owen was born 2 Nov 1828 in Kilskyre, Co. Meath, Leinster to Patrick Brady, 1790 - ? and Bridget Lynch, 1810 - ?. Owen died 19 Feb 1901 in Ransom, LaSalle, Illinois. Owen was my wife's 3 X great uncle and a brother of her 2 x great grandfather, James Brady (1827-1894).
Owen and Catherine had five children: John (1857-1942); Michael (1861-1935); Mary A (1868-?); Henry T (1868-1938) and Catherine (1873-1938).
Michael "Mike" Brady (1861-1935), married my wife's 2 x great aunt, Mary "Minnie" Noonan (1866-1895). Mike and Minnie had four children: Anna "Annie" (1889-1986;
Loretta Cathryn (1891-1992); Owen Sylvester (1893-1940) and Patrick Emmett (1894-1976). After Minnie died in 1895, Mike and his children moved to Emmet County, Iowa and later to Ramsey County, North Dakota. There are descendants still living in North Dakota, Oregon and Washington.
I hope that this helps to fill in some of the blanks for you, Terry. Let me know if I can help any further.