It wouldn't have lasted for more than a generation or two, because the Irish lords were too fractious and Scotland couldn't have comitted enough forces to keep them in line. Look how little success England, with greater resources, had during that period...
Aw, come on, I just want to throw my Graduate School training out the window and be a Romantic for a second
Honestly, very true, though. Although I could see the Scots being able to keep control of Ulster, which would have had some important, and interesting, ramifications.
So, lets do this:
*Edmund Bruce manages to unite the Irish and Norman Lords against the throne of England. Eventually, after a struggle, the Kingdom of Ireland is declared, subserviant to the throne of Scotland.
With the death of Edmund, the Kingdom begins to unravel; the Scots are forced to send resources down there and, over time, it just becomes too much; much of Ireland descends into anarchy. And yet, the Scots are able to maintain control of Ulster and the city of Dublin.
How does this effect the development of both nations, as well as England (with England's claims in France, I doubt they will be exerting much effort to really make good on any weak claims they have left in Ireland, and may well wish the Scots the "best of luck" in dealing with that backwater).