I set the Family Sharing successfully,and I want to share my Apple Music family sharing plan. But Apple Music is still asking me to set up family sharing.

Is the ID used for iTunes and App Store for the Music plan an administrator (parent or organizer) of the Family Sharing? This is a requirement.

I can't say I know exactly what your situation is but here are some tips.

1. The family member with the Apple Music Family Account must be an adult.
2. The family member with the Apple Music Family Account can use a different credit card for Apple Music.
3. The Apple ID for each family member needs to be the same for iTunes and Apple Music
4. If the other family members have their own Apple Music subscription (trial or paid) Apple Music Family Sharing will not work until their own subscription is canceled.
5. Log out of Apple Music when you get the Set up Family Sharing error message and restart the iOS device, then log back in. (Music Organizer, Family Organizer and others, starting with Family Sharing Organizer, then Music Sharing Owner / Organizer
6. Some have reported signing out of everything (Apple Music, iCloud and iTunes (if a Mac is involved) works. Best to sign all out first, then restart each device, then sign Family Organizer in, Then Music Organizer / Owner, then others after the first two can share Music.
7. Sometimes Family Sharing glitches during set up and you may have to remove everyone from the family and readd, starting with Music Sharing Organizer.

Let me know if any of the first three are causing problems and we can work on those.

Tip 4 means there is a conflict. The person with the free trial will not be able to join Apple Music Family plan until they are not in their own plan. When there is a conflict, Apple Music defaults to individual Music accounts and Music cannot be shared across Music accounts. This link explains how to cancel that redundant, unwanted Apple Music Account. But since that is not you, I would do that later. First I would focus on getting you and the Apple Music Organizer / owner up and running with the last three suggestions.

You should see just apple Music's normal screen like you do when you are subscribed to Apple Music as a stand alone member or the Music Sharing Organizer. When it works you don't get a message to that effect. You just get Music options. Your getting a sign up message means Apple Music is not registering for that Apple ID / device. Turning off/on the sharing of purchases for the Family Organizer as described above within the iCloud > Manage Family area should allow Music sync everything. When it works it takes a few seconds and my Apple Music for Family registers and the "Join Apple Music" just goes away.