I understand your usage, my family's set-up was similar; it just that it's different to Apple's vision of Music which explains why it doesn't quite offer the options you require.
You could always set-up Family Sharing, which would require all your family members to have a unique iTunes account.
This is how I've now implement our iTunes. Although there is one shared family Mac (ok, I have my own too), we all have our own user accounts, which enables individual iCloud syncing of Contacts, Pages document, etc. plus our own iTunes libraries (I simply imported the desired music from the 'old' shared iTunes library into each individual's account). You can set up Family Sharing so that each family member can share their purchases, plus it has the advantage of not having to 'see' music/apps, etc that you're not interested in. Plus you can enable 'purchase request' for your children's accounts, which is quite nifty.