Hi Emmy_uk,
Seems the family would need to have a Family Music subscription, for everyone to fully access Music. (Everyone in the family would be automatically included.)
If they don't have that, you could likely still download their iTunes purchases, if the family organiser has "purchase-sharing" turned on, (and therefore pays for everyone's purchases).
Music purchased from iTunes can generally be shared ok.
How to download apps and content that your family members purchased - Apple Support
If purchase-sharing is not turned on, everyone would pay for their own purchases.
Else:
What to do: If you can't find your family's shared content – Apple Support
All the best :-)