Seeing Marlene post here reminds me that I should've said that Queen Victoria's Descendants is, of course, a great source of information on Irene as well.
Hessian Tapestry deals with the whole Hesse family from the time that Alice married into it so it has a focus on Irene and her family that other books don't have. Even still, she's probably the least delved-into of the siblings. It was also written back in the 1970s, long before there was new archival material from the former Soviet Union, so it's a little out-dated. Nonetheless, it's one of my all-time favorite books and one I searched for in used bookstores all over the US (and in London on my honeymoon) until the advent of the Internet allowed me to find a copy. David Duff just had a great style of writing and it's a very enjoyable book.