They are all Irish names. For example, on Griffith's Valuation of Ireland, the names Hendren and Carroll occur together in Antrim, Armagh, and Belfast City. Her family had left Ireland by then though, so these locations might not help.
(Pronounce Hendren with an Irish accent and you get Henderhen. Like Rocky Road to "Dubalin". Or my grandfather's "Ballinatore" for "Ballintur". )
On the other hand, if her parents were both from one of those areas then it might be Patrick's family who are from Tipperary. Lots of Keatings in Tipperary on Griffiths. 225 families, more than 2x as many as anywhere else.
Your next stop is the censuses in that part of Illinois for Margaret's family. If she was really 27 in 1879, then she might have arrived with her parents.
Edited to add: because she would have married Patrick when only 17-18 or so. On the other hand, if she married on arrival she might have been on her own.
And for Patrick's family in Illinois also. The Thomas Keating in the household in 1870 is too old to be Patrick's child. He might be his brother, and he-Thomas-was born in Illinois.
The stop after that is Manchester births.
I hope to get back to this, but it won't be until late today, and maybe not even then.