I've been helping a friend with research on his Cassidy line. A brother and two sisters came to Chicago in the 1880's from County Cavan. A 1919 obituary says that there were also a surviving brother and sister in Co.Cavan. The US records give their parents as Patrick Cassidy and Bridget Riley. Using the Familysearch.org records and then the online records from rootsireland.ie, I found the civil registrations of the births of four children, Anne, Jane, Catherine & Henry, of Patrick Cassidy and Bridget Riley who lived in Annafarney townland. I think that the elderly Patrick living with his son Henry in the 1901 and 1911 census records is that same Patrick.
I am hoping to find a death notice in the Irish papers for Patrick which might mention the names of children living in the US. That's my next step.
You say that your Cassidy's came a little later to New York. I didn't know if that family had any memories or traditions of a Chicago branch.