The original requirement for a separate transatlantic carrier arose because BOAC/BEA had a shareholding in Aer Lingus (as part of a post-WW2 deal where Aer Lingus had a monopoly on Ireland (Éire)-UK routes). There were 2 UK airline representatives on the Aer Lingus board and they were generally opposed to an Irish transatlantic operation, ostensibly because it would be loss-making, but likely also because it would be competitive with BOAC. So Aerlínte Éireann was invented with a substantial overlap of its board with the Aer Lingus board.
In the original project with Constellations, my understanding is that the Aer Lingus and Aerlínte operations were somewhat separate though there were some Constellation oprerations on Dublin-Heathrow as Aer Lingus. A change of government cancelled that transatlantic operation shortly before it was due to start in 1948. The Constellations were sold to BOAC at a profit (as they had been bought before sterling devaluation and sold after it and the price was set in US dollars). That may well have made Aerlínte the first transatlantic airline to show a profit without a subsidy.
A second attempt with DC-4s hired from Seaboard and Western Airlines was blocked from the US end.
A thrid attempt, was sucessful, initially with Super Constellations flown by Seaboard pilots in 1958, graduating in 1960 to B720s flown by Aer Lingus pilots and then B707s and B747s. This was integrated operationally and commercially with Aer Lingus but using its own IN designator for the transatlantic sectors and was accounted for as a separate legal company. The British shareholding in Aer Lingus had been bought out in the 1960s, The designator for both airlines became EI about 1978.
In a subsequent reorganisation, the whole business was integrated legally as well as commercially and operationally. Aerlínte became Santain Developments Ltd and a dormant company. So far as I know, it remains in that state.