I am the primary for my family sharing but want to log in to apple music on my phone w a diff apple id

when i set up my family sharing i had everyone logged in to apple music using my apple ID. I want to allow my son to remain using my appleID but use my other apple id on my phone and macbook so that i can separate our music.

i went into settings, logged out of my main apple ID (the family manager one) and logged in using the other id. Somehow when i go into apple music it's still the other appleId and i keep going in a loop w clicking the ID and then logging in to the new id only to go back into apple music and the original ID is there.

I'm stumped.