I'm also related to an officer in the 23rd Illinois Brigade - Capt. James Fitzgerald of Co. I (Shield Guards) is my connection. Capt Fitzgerald was born in Co. Limerick, Ireland.
I would recommend reading "Shades of Green: Irish Regiments, American Soldiers and Local Communities in the Civil War Era" by Ryan Keating. That book focuses on the Irish ethnic units from Chicago, Wisconsin and Connecticut. I'm in the middle of reading it myself and am excited to find this resource. I see Keating actually mentions your relation on the chapter re: Mulligan's Brigade..."...Although the company eventually filled their ranks with men from Chicago, Detroit, and Milwaukee, Ottawa residents Charles Coffee, Thomas Hickey, and James Hume retained command of the unit."...and he also quotes a letter that Charles Coffee wrote home..."Hearing of these efforts, Charles Coffee wrote home that 'the Havelocks which you propose to send us will be a welcome gift our company now numbers ninety men, out of which sixty four are from LaSalle County." Furthermore he noted, 'the ladies of Chicago are now preparing the same article for all the Companys of the Brigade that were organized in this City - and I do assure you sir, and through you the Ladies of Ottowa, that it is with no small pride that we know that the 'Ottawa City Guards' are not forgotten by the fair daughters of the City from which we proudly take our name.'"
I live in Iowa. If you'd like me to go to Butler County to see if I can find Charles Coffee's gravestone, I'd be happy to do that for you.