In the far left column of this page, we find the Mulcahys, in the same district of the 12th Ward as Mary's parents. Michael is 32, Irish-born, and his occupation is "Liquors." Mary is 22. Their two children (thus far) are listed as Maggie (Margaret Mulcahy Hennessy) and James. Maggie is 3, and James is 1.
One thing this does show is that the Mulcahys weren't living at 85 Luqueer St. while Matthew Madigan was alive. Given that, I really continue to wonder how they ended up living there, while his wife and minor daughter end up in an apartment around the corner. I may - emphasize may - have come across notice of proceedings on the estate of Matthew Madigan. Following up on that is something I intend to do, though it will (I think) require a trip to a Brooklyn courthouse, which itself will require taking a day off work. But I'm getting there. And we'll figure it out eventually.
But that's really all the information we find here. Why does it excite me so?