Hello Hankern71,
Thanks for asking the Apple Support Communities about playing Apple Music.
Apple Music can be played on any device using your Apple ID, but the individual membership allows music to only be played on one device at a time: Join Apple Music on your iPhone, iPad, iPod touch, Mac, or PC - Apple Support
"You can listen to Apple Music on any device that's signed in with your Apple ID."
If your granddaughter is not listening to music, have her close the Music app and you can listen to music on your device. As you mentioned, an alternative is an Apple Music family subscription: Get an Apple Music family subscription - Apple Support
To do this, you can get a child Apple ID for your granddaughter if she meets the age requirements: Family Sharing and Apple ID for your child - Apple Support
"To participate in Family Sharing, all family members must have their own Apple ID. Children under 13* can't create an Apple ID on their own. However, the family organizer can create an Apple ID on their child's behalf. "
You will then use your Apple ID to set up the Family Group, and invite her Apple ID. Use your own Apple ID for Family Sharing - Apple Support
To ensure she can't make make purchases on your payment method since you will be the Family Organizer, enable Ask To Buy: Request and make purchases with Ask to Buy - Apple Support
Cheers.
