Gelman, Andrew, and Jennifer Hill. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, 2007, is not about GLMs per se, but also covers that and has a nice mix of theory, hands-on-advice, implementation in R, and exercises (and, when you websearch for it, you might find an ebook version of it!).

Not a textbook, but freely available is this graduate statistics course from the Harvard Government Department, which also covers the most common GLMs. The section videos cover implementation in R. The textbook is King, Gary. Unifying political methodology: The likelihood theory of statistical inference. University of Michigan Press, 1989.