The Normans in almost no way invaded Ireland the way they did England. In 1170/71 they arrived under firstly Richard Strongbow then Henry II. Remember this is 1171 but no fighting was done and the Irish lords paid their fealty. By 1394 the local Irish lords and chieftains still owned the vast majority of Ireland particularly after the Black Plague had decimated 1/5 of the Irish population between 1348-61: the more highly populated English towns taking the biggest hammering. Ireland took a LONG time to be tamed. I mean sure, they were there to stay and set up their own systems and laws but I'm not entirely sure what you were told that the church supported?

Anyway this is where I'm finding fault at narrowing down your question. In David Ross' book "History of a Nation" he notes how not until the 17th Century could the King Visceroy in Ireland claim any sort of hegemony over the Island.

So the "Norman Invasion" of Ireland isn't really a thing the way it is for the UK. There was no significant resistance against Norman reign as the landings in both 1171 and 1394 were met by submission from the Irish lords themselves so the Normans had no need to come inland and subdue the Irish citizenry until much after the original "invasion." Is it this time you're speaking of?