From the Irish Press Newspaper, a few days after her death at Sir Patrick Dun's hospital :
Saturday 3rd May 1941, Page 3
"Death of Mrs. Gilmore
Mrs. Frances Gilmore, Ballygawley, Dundrum, Co. Dublin, who died in Sir Patrick Dun's Hospital, was mother of Mr. George Gilmore, well known in national and labour circles.
Mrs. Gilmore, formerly Mrs Angus, was a native of Howth where her family have been connected with the lifeboat service for many generations.
She was imprisoned in Kilmainham in the civil war.
Mrs. Gilmore is survived by her husband, Mr. Philip Gilmore, George Harry, Charles Gilmore (sons) and Miss Dorries Gilmore (daughter). The funeral takes place to Howth to-day"
The mention of the civil war confirms the possible 1922 timeframe you have, as the civil war started in mid 1922.
FindMyPast has prison registers for up to about 1924, including some records for Kilmainham, but dont seem to cover 1922/23 for that prison. If there are records available for the prison for that period then they would likely be held in the National Archives. Martial Law was in place from September 1922 so the alleged office might not have been processed though the regular courts system.
There are various articles online including one on Wikipedia about a George Gilmore of Dublin, presumably son of Frances & Philip, who was involved in the War of Independence and the Civil war on the Anti-Treaty side. He is mentioned in connection with incidents up to at least 1926, and imprisoned a number of times up to about 1932.
EDITED : according to the Kilmainham Gaol Museum website the registers for the civil war period do not survive.