Sadly I think you'd pretty much need 1920's PODs to change how things played out, either that or Sealion. As I've said in another site, basically nobody would want to have the circumstances that gave birth to the Irish military and Governmental policy if they could chose to avoid it.
Understood.
Given where you are, what would you think about a larger "Irish" formation in the British Army, presumably with the intent of giving a "home" for volunteers and making a deeper connection (to the British advantage, of course; its a cynical play) between the NI/UK/"British" populations and the Eire/Republic/"Irish" population?
As it was, the British - upon Churchill's direction - created the 38th "Irish" Brigade in January, 1942, with a brigade headquarters formed from the infantry training organization and three battalions, 1st Royal Irish Fusiliers, 2nd London Irish Rifles, and (initially) 6th Inniskillings, replaced by the 2nd Inniskillings in 1944. The 1st RIR and 2nd RIF were both regular battalions, the 2nd LIR a former territorial battalion. The initial brigade commander was Morgan John Winthrop O'Donovan, MC (The O'Donovan), and he was followed by Nelson Russell (Antrim-born) so there was a point being made... the formation patch was kind of obvious, as well.
The brigade was used to build up the 1st Division in 1941-42, transferred to the 6th Armoured Division in June, 1942, and served as such in North Africa and Italy, with a distinguished record, and as part of (most of the the time) the 78th Division, which despite the high number was a largely regular division.
So, granted that "Irishness" was a matter of self-identification by a large degree in the British Army by this point, but: there were still four "Irish" infantry regiments in the British Army lists (Irish Guards, Royal Inniskilling Fusilers, Royal Ulster Fusiliers, and Royal Irish Fusiliers; each would have had at least two regular battalions in 1939, and with various territorial and wartime activations), and well as the London Irish Rifles from the Territorial Army, I think there were at least 12 "Irish" battalions that saw active service outside of the UK in 1939-45.
Given enough willingness to transfer battalions around, presumably the British could have concentrated 10 infantry battalions and a cavalry/recce regiment (North Irish Horse, presumably) to form a full infantry division on the standard organization (three brigades of three battalions, plus an infantry machine gun battalion), it would have been possible - if it was a matter of policy - to reactivate one of the three WW I era "Irish" divisions (10th, 16th, or 36th) for WW II. (The actual WW II 36th Division was not "Irish" and given the "Ulster Division" sobriquet from WW I, maybe not a good choice.) The 10th and 16th were both activated in 1914, and each had their own political background...
So if Churchill orders the 10th "Irish" Division to be reactivated early in (say) 1942, largely from exiting units, and they can be reshuffled, what are your thoughts on how that would be perceived in Ireland (north and south)?