Although tens of thousands of Irish nationals (including many deserters from the Irish Defence Forces) joined the British armed forces during the Second World War, most were too young to have fought against the British in the War of Independence, it seems. Patrick O'Daire thus strikes me as something of an anomaly. However, two other IRA veterans deserve mention:
Thomas Finucane, a survivor of the Easter Rising who later emigrated to Britain, purportedly gave up on his attempt to serve as a teleprint operator for the RAF due to his wife's objections; but their three sons did enlist in the British armed forces, and one of them, Brendan ("Paddy"), went on to become a RAF fighter ace.
Charles Russell, a founder and former head of the Irish Air Corps, approached the British government in his retirement with an offer to help raise Irish units. The British turned him down, as they did not want to risk damaging relations with Ireland and therefore lose access to the Irish manpower that they were already tapping into.
Conversely, some of the leadership in the Irish Defence Forces had previous experience with the British military, most notably Anthony ("Tony") Teasdale Lawlor and James Morris (a.k.a Séamus Ó Muiris). The former served in the First World War as a member of the Royal Flying Corps, from which he was eventually invalided out. As an officer in the Defence Forces, he headed the Armoured Car Corps (later renamed the Cavalry Corps) throughout much of the 1930s and 40s, with a brief stint as commanding officer of the embryonic Marine and Coast Watching Service from January 1940 to May 1941 (his personal interest in maritime matters appears to have been his main qualification for this assignment).
Morris, born of an Irish family in England and a graduate of the Royal Naval College at Dartmouth, saw action in the Battle of Jutland while aboard the dreadnought HMS St Vincent. In 1920, after being appointed second-in-command of light cruiser HMS Castor, he resigned from the Royal Navy in protest of the treatment of Irish political prisoners, many of whom the Castor had transported to internment. He succeeded Lawlor as head of the Marine service in May 1941, having written repeatedly to the Irish government in years prior about the importance of establishing a navy.
Sources:
Steven O'Connor, Irish Officers in the British Forces, 1922–45 (Basingstoke: Palgrave Macmillan, 2014), 172f.
Eunan O'Halpin, Defending Ireland: The Irish State and Its Enemies since 1922 (Oxford: Oxford University Press, 1999), 168f.
The information on Lawlor and Morris comes from my notes; I can supply sources once I get back home in a few days.