The Good Friday Agreement 1998 set up a Northern Ireland Assembly to govern the region. This is a devolved assembly subordinate to the British Parliament. The Assembly parties form a coalition executive under a First and Deputy First Minister. Cross border institutions were to connect Northern Ireland departments with their equivalents in the Republic.

The Republic of Ireland agreed to remove its constitutional claim to Northern Ireland and replace it with recognition of the right of the majority of Northern Ireland to decide its future.

Several reforms were included but put in the hands of separate committees or measures. These included police reform, the decommissioning of paramilitary arms and the release of prisoners.

You seem to be suggesting, from the first part of your question, that Britain simply conquered Ireland, taking it over as a possession, as it were. If Britain had done that, then the problems associated with the relationship between the two would have been very much simpler. These books are quite good at explaining the means by which a few Anglo-Normans and their followers became briefly dominant before becoming part of the inchoate Irish polity. Early Medieval Ireland, 400-1200 (Longman History of Ireland) O Croinin, Dáibhí, Ireland in the Age of the Tudors, 1447-1603: English Expansion and the End of Gaelic Rule (Longman History of Ireland) Ellis, Steven G., Gaelic and Gaelicised Ireland in the Middle Ages (History of Ireland) Nicholls, Kenneth.