If any of the music is available as an MP3 download, you could also manually download the MP3 "DRM Free" version, and then just import it to your wife's library. That's why I have been buying my music from amazon instead of Apple, pretty much all of the stuff from Amazon is DRM free so if you don't want to go through the trouble of setting up the family sharing, you can just download the MP3 files and manually import them. Works great in iTunes, just copy the music in it's own folder to the iTunes music folder and tell iTunes to import that folder.
If it's an MP3, iTunes assumes you own the license to listen to it so there's no hassle involved. And because both iTunes and Amazon have family sharing for a limited number of accounts and playback devices, it's legal as long as you don't share it outside of their allowed limits.
That said, I recently linked my wife's amazon account to mine to share digital media. It's pretty simple and as others have pointed out, it's not terribly difficult to do it with iTunes either. The only difference is that the apple DRM will prevent you from copying the music to random generic devices. Of course, you DO have the option of burning a digital music CD with iTunes that will convert even DRM iTunes music to MP3 files for the purpose of archiving them on CDs or DVDs. Once they're converted to MP3 format, anyone can import them to their library. Again, don't abuse it and it's completely legit and legal. That's the other way to put iTunes music on non-apple devices that fit within their definition of allowable use. iTunes just kind of hides the option to convert to MP3 in the burn to CD feature.