Northern Ireland won't split from Great Britain. Too many people there are too heavily invested in their identity as British and would happily follow the rest of the UK over the edge of a cliff so long as they get to keep their Union Jacks and framed photos of the Queen.
Sinn Féin have called for an Ireland-wide referendum on unification because obviously they have. Even if you grant that they don't have the ulterior motive of being Irish Republicans and that they genuinely want Northern Ireland to remain part of the EU (and there's no reason both of these things can't be true), that's probably the only way to ensure that the six counties of Northern Ireland do remain part of the EU in some fashion. And, of course, if it did pass, you'd simply end up with a resurgence in sectarian violence as Unionist hardliners rebel.
You're probably right on all counts apart from leaving Great Britain (though its's also possible you're right on that too). As an Irishman I'm not sure a united Ireland is desirable as the problems of the north may spill into the south. I would personally support an independent Northern Ireland in the EU more than a united Ireland.
Sinn Féin have called for an Ireland-wide referendum on unification because obviously they have. Even if you grant that they don't have the ulterior motive of being Irish Republicans and that they genuinely want Northern Ireland to remain part of the EU (and there's no reason both of these things can't be true), that's probably the only way to ensure that the six counties of Northern Ireland do remain part of the EU in some fashion. And, of course, if it did pass, you'd simply end up with a resurgence in sectarian violence as Unionist hardliners rebel.