Google does not allow music that you've purchased in your Google Play Music account to be shared. However, if you use Google Nest or Google Home speakers you can work around this limitation.
Let me introduce you to Mary and Bob and their daughter Alice. Bob has hundreds of albums in Google Music. Mary has a few albums of her own, plus many childrens albums that Alice likes to listen to. Here's how to set up the speakers so that Mary, Bob and Alice can all request the childrens albums.
If the speaker can identify who is talking then it will only play music from their Google Music account. If it cannot identify them it will play music from the account of the first person who set up Voice Match within the Google Home App (more info). In this household, Bob initially set up the speakers, so his is the default account. We need to change this to Mary, but there is not currently any straightforward way of doing so. What can be done is to reset the speaker completely, then get Mary to set it up.
Now, Mary and Alice can ask for nursery rhymes from the speaker, and they will come from Mary's account. Bob can ask for his own music, or he can put on a silly voice so that Google does not recognise him, in which case he can access Mary's music too.