Whilst Connaught was one of the four provinces, I think you will find there is a place called Old Connaught between Dublin and Bray. I don't think you'll find the family moved to Rochdale as Mary Snr, Annie,Mary Jnr John and James were still in Congleton 1881 at 4 Holford Street and Thomas was in Hulme already not a milion miles from Rochdale. In 1901 James is in Monks Coppenhall and John in Burslem You might have a chance if one of the girls married and Thomas was a witness so you could compare signatures. There was a Kenny family in Rochdale anywayby the look of things. Were they related ?