Welcome to the Apple Support Communities!
I understand you have an iTunes Family Sharing account set up and you would like to add an Apple Music Family membership so that your kids can enjoy the service. To do this, you will need to create an individual Apple ID for each of your kids, and then invite them to join your Family. If any of your kids are younger than thirteen, you can create an Apple ID on their behalf. I'll include a few resources below to help you with this. I've highlighted some key information here for you. Click on the links for complete details.
Set up Family Sharing
Family Sharing makes it easy for up to six people in your family to share iTunes, iBooks, and App Store purchases, an Apple Music family membership, and an iCloud storage plan, without sharing accounts. When the family organizer turns on purchase sharing, you can pay for family purchases with the same credit card and approve kids’ spending right from a parent’s device. Family Sharing also lets you share photos, a family calendar, and more to help keep everyone connected.
Each member of an Apple Music Family subscription gets unlimited access to the entire Apple Music catalog, music recommendations tailored to their personal music tastes, and access to their own iCloud Music Library, which makes it possible for them to listen to their music on all of their favorite devices.
After you set up Family Sharing, you can invite additional family members to join your family group.
After the invitees accept your invitation, each member of your family group will have access to Apple Music.
If you already subscribe to Apple Music, you can change to a Family Membership in the Music app or in iTunes on a computer. Learn how to manage your Apple Music subscription on your iPhone, iPad, iPod touch, Mac, or PC, or on an Android phone.