Re: I accepted Apple Music invitation but it is not reflecting on my Apple Music app. Keeps asking me to subscribe
To check if your access to the Music subscription is enabled:
Share Apple and App Store subscriptions with family members on iPhone - Apple Support
Check you are signed in (to your device) with your Apple ID: Sign in with your Apple ID - Apple Support
Then check if this works for you:
Open the Apple Music app and tap Listen Now.
In the top-right corner, tap the photo icon.
Sign in with your Apple ID and password.
Seems everyone has their own library, to which they add the music they want to hear.
Previous purchases may be available in the "Library" in the Music app.
or
If needed: How to: Redownload music - Apple Support
What to do: If you can't find your family's shared content - Apple Support
Music Support Website:
Music - Official Apple Support