Pat, unfortunately I have NO recommendations! I'd hoped more from this ( and I liked the cover too ) because my particular knowledge is limited to old articles in Civil War Times Illustrated and books and visits to places like Fredericksburg and Gettysburg. I was disappointed in this mainly because the battle accounts are merely a rehash with almost NO emphasis on the actions of the brigade itself. I know there are classic accounts of the brigade and memoirs by its members though. If you have any knowledge about this book I'd like to know what you thought about its accounts of the tribulations leading to immigration as to accuracy because I thought maybe that was its only saving grace; the military side certainly wasn't.
I used the Bilby book a few times, it has some good research in it, but I have some real problems with it. I am encouraging the Irish historian Damian Shiels to do a full history of the Irish Brigade since he has done a lot of research on it over the last three years.
I would heartily recommend Irish Green and Union Blue: The Civil War Letters of Peter Welsh, Color Sergeant, 28th Massachusetts edited by Lawrence Kohl and Margaret Cosse Richard published by Fordham University (1986). However, these letters are often more concerned with why he fought rather than with the battles themselves. I believe Welsh may be the most quoted immigrant of the war as his letters have been quoted by just about every major historian who touches on the subject.
William McCarter's memoir
My Life in the Irish Brigade: The Civil War Memoirs of Private William McCarter, 116th Pennsylvania Infantry is wonderfully written by an Irish Brigade recruit who was badly wounded at Fredericksburg. Unfortunately, his service with the Brigade only lasted four months. But if you want a real look at the soldiers point of view during that one battle, this is it.
The Story of the 116th Regiment: Pennsylvania Volunteers in the War of Rebellion by St. Clair A. Mulholland (1903) is well written by an officer of the Brigade. It has a limited focus because the 116th missed the first half-year of the Brigade's existence. Mulholland himself is a good writer and he commanded the regiment after the death of its first colonel. You can read it here for free online
http://www.archive.org/stream/storyof116thregi02mulho#page/n9/mode/2up
Many of the stories you read in most histories of the Brigade come from the 1867 Irish Brigade history by David Power Conyngham's
The Irish Brigade and its Campaigns (1st Edition 1867). If you follow that link you can read it for free. The problem with it is that the author did not join the Brigade until 1863 and so his early accounts are written from others reports.