Yes, I think we do have a link.I have your Ann listed from the 1881 Census living with James, his second wife Margaret, younger brother David & stepbrother Joseph.I have a copy of my Margaret's birth certificate which gives her mother's name as TIERNEY.As with some other names in the family, say it with an Irish accent in Chester & you'll get some very odd spellings!
Maggie as she was called, married William AIRTH in 1884 in Chester.They had 11 children, 4 boys & 7 girls.All the boys died before they married (Edward James was killed in WW1).I am desended from the eldest daughter, Mary Elizabeth AIRTH b.1887, who married William Henry UNDERWOOD in 1911 in Chester.
I would love to know where in Ireland James & Catherine came from.Other McAndrew's in Chester on the 1901 Census may be James' brothers & they give their place of birth as Co Mayo, Ireland.I don't know what happened to James or where Catherine is buried. I have yet to find a registration of her death.
Would love to hear more from you! best wishes, Siân