The problem is not that the UK considered Ireland to be a dominion, or even what the Irish considered themselves. The problem is that, if you make Ireland a dominion in-game, it will behave like a dominion in-game.
For example: the UK player opposes Rhineland, goes to war in 1936, and calls the dominions. Either Ireland behaves like a dominion and goes to war, or it behaves like Ireland almost certainly would have done* and wishes the UK good luck with all that, remaining neutral. If, through national spirits and/or hard-coding the Irish AI, they pursue the latter course, why bother making two layers of additional coding (first to make them a dominion, then to get them to behave unlike a dominion), just to get exactly back where we are now?
In a potential future DLC involving Ireland, it might be useful to explore the possibility of reworking the entire dominion system so that Ireland stays out of the UK's foreign entanglements, or perhaps to create a national spirit of "Special Dominion Status" or some other such thing to model the very complicated way the UK and Irish Free State interacted until the establishment of the Republic. As it stands now, it is more useful to portray Ireland as fully independent.
*To sum up, skipping a lot of details: Éamon de Valera was the party leader for the largest political party in Ireland during the entire period the base game covers (Fianna Fáil) and President of the Executive Council for the Irish Free State in 1936. de Valera had already forced out one royal Governor-General and begun a
trade war with the UK over provisions of the Anglo-Irish Treaty, and was looking to end that treaty completely and establish an Irish Republic, which he did by 1937. I humbly submit that there is literally no way that de Valera or Fianna Fáil would go along with any kind of UK wars, allow use of the National Army, or even give favorable trade terms (not that Ireland has useful trade commodities in-game) under that government, all three of which the other dominions are basically hard-coded to do.