Hopefully someone else can recommend a book that covers the whole century, but I can suggest a few that concentrate on the first quarter of the century, which I'd say is the most 'interesting' and divisive period in the Anglo-Irish relationship:

Dividing Ireland: WW1 and Partition, Thomas Hennessey 1998

This gives a great overview of the collapse of the Home Rule Act because of WW1, which is perhaps the pivotal issue, along with good coverage of the 1916 Easter Rising and the conscription crisis in 1918 (as a response to the massive German offensive of March 1918, the British Government prepared to extend conscription to Ireland, with even clergymen and religious ministers to be conscripted alongside boys of seventeen. The Sinn Fein Standing Committe called this action 'a declaration of war on the Irish people' in their Orders on 17 May 1918. The tide of fortunes in WW1 turned quickly, thanks especially to the growing numbers of American servicemen arriving on the Western Front, and the German offensive was halted. Conscription plans for Ireland were dropped in June, but the damage was done.)

"An armistice has been signed in France; but in Ireland there is no armistice." An t-Óglách (Journal of the Irish Volunteers), 30 November 1918

Ourselves Alone: The Green Flag (Volume 3), Robert Kee 1972

This gives a very thorough account of Irish Nationalism and the run up to the Rising, the Anglo-Irish War, Partition and the Irish Civil War.

If you have an interest in the Anglo-Irish War in particular, I'd recommend these two books:

A Hard Local War: The British Army and the Guerilla War in Cork 1919-1921, William Sheehan 2011

The Black and Tans, Richard Bennett 1959