No family in Ireland is not in some way connected to these events and organizations.  Conor Cruise O'Brien has an article in the Atlantic Monthly which vividly demonstrates the concomitant complications. My own paternal great-grandfather fought in the Easter Rising and the War of Independence and was interned by the authorities where he continued his protest by going on hunger-strike.  Bernard Reid,  my first cousin twice removed, also a Nationalist, was a founding member of the 1913 Irish Volunteers, an armed body dedicated to protecting the legitimate rights of the Irish people to self-determination. All subsequent Irish armed organizations, from the armed forces of the Republic of Ireland itself to contemporary terrorist groups, can trace their origins in these Volunteers.  Their aim was to protect the implementation of "Home Rule", parliamentary legislation then nearing enactment which would mean Ireland's devolution (though not complete independence) from Britain.

After several skirmishes with Crown forces, events in Ireland were overtaken by those in Europe.  War was declared and Home Rule for Ireland shelved.  An understanding was reached
between Moderate Nationalists and the British government that a common front against Germany for the duration of the war would ensure Home Rule once the conflict (then, of course, envisaged as
a matter of only a few months) had been concluded.  At this point the Volunteers split.  It is said some 100,000 Catholic Irishmen (many guided less by political allegiance than by sheer economic
necessity) fought in British uniform on the continent.  Irish Volunteers who chose to stay at home - among them Padraig Pearse, Eamon de Valera and Michael Collins - went on to become the
patriots of 1916. Meanwhile my cousin was to die a British Soldier on the Western Front, a matter of weeks after the Rising in Dublin.

The political reasons for the extraordinary circumstances of Bernard Reid's death are complex.  It was understood that Irish soldiers willing to fight Germany would ensure devolution for their country once the wretched business was concluded.  However Bernard Reid went to the Front mainly to defend France.  Though a French speaker his application to the French Foreign Legion was
postponed (as a British subject,  French authorities argued, he could volunteer for the British forces.)
 
You might look at the following, far from exhaustive, bibliography for more on the various subjects touched upon at this site:
 

Ireland and the  First World War/Fitzpatrick, D. (Ed)
The Ways of War/Kettle, T. [OP]
Orange, Khaki and Green
Ireland 1912-1972/Lee
The Experience of World War One/Winter
Celtic Dawn/O'Connor
Ireland, a Concise History/Cruise O'Brien
The War in the Trenches/Lloyd
All Quiet on the Western Front/Remarques
Distant Drums/Dungan
Dublin 1913/Curriculum Development Unit, TCD
The Insurrection in Dublin/Stephens
General Richard Mulcahy/Valiulis
Eamon de Valera/Coogan
Michael Collins/Coogan
The Years Flew By/Czira
The Great War and Modern Memory/Fussell