You should not have to wait for the trial to end. According to:
Get an Apple Music family subscription - Apple Support
"If someone in the family group already has an individual or student subscription to Apple Music, renewal of that subscription is automatically canceled when they join the family group."
Did you follow all the steps in the above link, including:
Set up Family Sharing - Apple Support
If so, you might be able to fix your issue by turning Sync Library off for all of your devices, then turning it back on again. Learn how.