Thank you again Carol. It looks like it fits, but of course looking like is not proof. I guess the best record to get would be Maggie Cousins (nee White)'s immigration record. That way I'd get a better idea of her year of birth; and I'd also see if at the time she was already married to James Cousins (so probably immigrated 1882/4 like him) or travelling with her parents Nicholas & Catherine (who must have imm to US from Wexford sometime between 1878 and 1901).
The 'backward names' don't worry me so much as they could be transcription errors. I found her brother John's 1908 passenger record in two places - one with the correct name for his father and the other an incorrect name. Haven't found any record for his time in Butte, Montana though.
This Maggie also had a sister Mary b.1863 who has never turned up anywhere. I suspect that by the time her parents returned to Ireland she was already married in US.
Thanks a million for your help.