What I would like to see:
Build T2 west of T1 between 10L/28R and 10R/28L. Spec for narrow body locos and charters. A barn for planes (like STN).
Remove all non-interlining airlines from T1. Use the space freed up to rebuild T1 as a proper terminal with whizzbang new facilities like being able to transfer between flights without going landside.
Build the DART spur from the Belfast line near Howth Junction to the Navan line near Hartstown, east-west with stops at T1 and T2 and/or build a DART-spec metro line from somewhere near Balbriggan through Swords to T1 where it intersects the DART Spur. This line to continue to O'Connell Street and preferably St. Stephen's Green or further south.
[why give a damn about rail connections, especially west of EIDW? Read the Fingal Council planner's report on 10L/28R and you'll see.]
As to who should own it? The airlines and the DoT should draw up the specification required and all parties including DAA tender for it.
However, I think competition between terminals is less important - let MOL have his shed because all he will do is moan all through the process about "gold plating" if full-service airlines use T2 and require more services than he wants to provide. It's probably better for one authority to be responsible for the airport as a whole than have the shenanigans one reads on D&G relating to SYD.