This seems to be the family in 1901
http://www.census.nationalarchives.ie/pages/1901/Galway/Wormhole/Garrynagry/1395047/By 1911 Michael is deceased and Mary Senior is shown as a widow with Patrick and Catherine.
If attempting to contact religious orders I would start with the Sisters of Mercy who have a convent in Oughterard since the 1860s which would be a logical place to join before leaving home; otherwise without a clue it will be difficult.
In an attempt to work out which sister may have been the nun I looked at possible marriages for both to rule one out.
A very good possibility as a relative is:
Mary DARCY marrying PATRICK CRIBBIN in 1903
Civil Record Reference: Oughterard Oct-Dec 1903 Volume 4 Page 149
This seems to be them in 1911
http://www.census.nationalarchives.ie/pages/1911/Galway/Letterbrickaun/Leenaun/469666/The age is correct and the civil certificate would confirm if she is the correct sister.
There is a death in 1953 that could be her
Civil Record Reference: Mary CRIBBIN Oughterard Jul-Sep 1953 Volume 4 Page 181
There is also a marriage for a Margaret DARCY in 1910 in Oughterard
Civil Record Reference: Oughterard Jul-Sep 1910 Volume 4 Page 165
There are 4 possible spouses of which two I have ruled out as their wife on the 1911 census
is not named Margaret or a derivative; leaving a Hugh Walsh and a Pat Toole
whose families are not obvious in 1911.
As there are only two Margaret Darcy's of marrying age on the 1901 census this is a good possibility;
again getting a cert will confirm or deny
It may be that the relationship was incorrect in family lore i.e. great-aunt
I looked for quite a while for a supposed aunt of my grandmother who had married a landed gentleman allegedly! It turned out it was my great grandmother's cousin who was the person in question!