How do I set up the Apple Music family plan if we all have different Apple ids

That is exactly how it is supposed to work. As the instructions here:

Get an Apple Music family subscription - Apple Support

say "First, set up Family Sharing".

Then in:

Set up Family Sharing - Apple Support

"Family Sharing makes it easy for up to six family members to share App Store purchases, Apple subscriptions, an iCloud storage plan, and more—all without sharing an Apple ID."

That's how Get an Apple Music family subscription - Apple Support