One of the problems, as I have said in the other place, is that Ireland hasn't a lot of minerals relatively speaking, compared to Wales or Scotland or any of the regions of the UK other than East Anglia. So any local dominance is going to wane from the mid 1700s on and totally fade by the full Industrial Revolution, even with a fractured England. Ireland in that scenario would be a sort of Sweden, a historic Power but no longer quite powerful enough to dominate its neighbours.
Possibly a situation where the different groups that invaded Britain after the Roman fall are more linguistically diverse and Great Britain ends up with a Gaelic speaking Scotland; a Norse speaking Northumbrian Kingdom; a Danish speaking Kingdom of Jorvik (Yorkshire and Lancashire) a Frisian speaking Angleland (Lincolnshire, Norfolk and Suffolk); a Mercia speaking a descendant of Anglo Saxon; a Greater Kernow encompassing Somerset and Devon and speaking Cornish; Wales speaking Welsh; and a Southern English Kingdom speaking another separate descendant of Anglo Saxon with Breton, Cornish, Frisian, French and German loan words?