Could it be possible, in an alternate Good Friday agreement or earlier, for an effective condominium in Northern Ireland, with both Ireland and the UK sharing power in the region (even more so than OTL), and Northern Ireland sending MPs to both the House of Commons and the Daíl? It could be interesting to have the UUP as the SDLP analogue in the Daíl and the DUP as the Sinn Fein analogue.
Just outside my work, every Saturday, there are people who protest that the Union Flag is not being displayed 365 days a year over the City Hall.
This change happened in 2011.
The flag flies more often over City Hall now than it did at Stormont then or now.
That is how committed Loyalists are to ensuring that Ireland isn't united. I've seen TLs on this site where Churchill hands over the six counties if Ireland joins the War, and there isn't a whimper. These people barely thirty years before were publicly threatening to shoot British soldiers if they were under
Home Rule. The amount of Catholics who are pragmatically Unionist when it comes down to it is about half and half. It is almost unanimous that Protestants are Unionists, and very few care about any economic arguments; it would be like trying to convince England people to become a part of America based on economic interest. People outside of Northern Ireland often badly underestimate the absolute fanaticism within Loyalists, or think its equivalent to the Republican movement in Northern Ireland. Loyalists are on permanent paranoia that at any moment all their culture is on the verge of being swept away, or outlawed; at this point Loyalists have never been so on edge, yet the support of the Union has never been stronger in Northern Ireland, and the turnouts at Loyalist festivals and bands are as high as ever. Northern Irish Loyalism * is an ideology awash in paranoia, especially towards Westminster, whom they fear are out to sell them down the river.
It took more than forty years of state pogroms, state discrimination and Sectarian marches through their own streets, a Civil Rights Movement being rejected by Stormont and then ignored by Westminster, for Republicans to launch widespread rioting in the region. Bare in mind, that's just starting from 1921; you can easily find centuries of abuse if you keep going back.
It took a flag being raised on fewer days on a City Hall for Loyalists to launch widespread rioting in the region.
Any attempt to give serious power to Dublin over Northern Ireland without referendum (bear in mind, Thatcher shoved the Anglo-Irish Agreement, an exceptionally moderate treaty, down N.I.'s throat because she knew it would lose said referendum) would result in the UVF and UDA going into Doomsday mode, the results of which would not be pretty, especially for Catholic civilians. The UDA actually published what they would do if abandoned by Westminster, which consisted of interning the Catholic population as ransom.
So no, any attempt to give Dublin more say over Northern Ireland would be rejected in the Good Friday Referendum, and would embolden Loyalists to commit more indiscriminate violence.
* NB: Loyalism is not Unionism; the latter is a moderate position, the other is awash with people fighting the same battles as a few hundred years ago.