The Triunes will be the victims of their own success. When this war is over, initially a lot of funding will be needed to restore the conquered territories. I guess that projects in England and Ireland (or at least in Northern England) will be underfunded or cancelled already. Add to that the increased weight of the "continental" part of the Triune realm and you have a recipe for rebellion. All it takes is a less than average monarch, or a more than average rebellion leader . However, without support from the outside, I don't think a state comprising of Northern England and Scotland is viable. If however all of England rallies behind the rebellion then things could be different, taking into consideration the fact that England dominates the Triune navy.
Finally, there is the colonies parameter . The colonies are dependent on the navy for growth (more immigrants) and trade. Maybe in the case of a Civil War they would choose to side with those controlling the Navy. And their increased vulnerability would tempt some other powers like the Spanish to take advantage of that.