Books on complex dynamics that discuss polynomial mating?

I don't think that such a volume exists, but let me try and give some helpful references nonetheless. Use with caution: my knowledge of the literature is somewhat out-of-date.

• There is a very brief mention of polynomial mating (see appendix C9) in volume II of Hubbard's wonderful series on Teichmüller theory, but this appendix is focused on the Sullivan dictionary so may not be quite what you are looking for. (Presumably you're already aware that Hubbard's series is an excellent general reference.)

• Bonk and Meyer's book on expanding Thurston maps seems to have finally been published (see also the arXiv version). As with the example above, the book contains a brief discussion of polynomial mating but the primary focus is elsewhere.

• As you presumably know, Milnor's book doesn't talk about mating at all, but he does have a lengthy expository article working through an explicit example.

• My favorite expository article on mating was Petersen and Meyer's "On the notions of mating". As you may know, there are a bunch of different notions of what mating is, and I found this article supremely helpful in keeping them straight, providing some proofs of foundational topological results, and pointing to the various parts of the research literature for each notion.

• I think Sarah Koch has some notes from a topics course on complex dynamics focused on the topology and dynamics of rational maps that talk about polynomial mating, but I can't find them anywhere. (The homework questions from that course may be independently useful to you.)

Unfortunately I think you're in that common-but-awkward situation where the topic is a little bit too specialized for a first-course-in-complex-dynamics treatment (even if the author has a particular interest in the topic), but nobody's yet written a special-topics-course-like treatment (with the possible exception of Koch's notes mentioned above). Best of luck!