How to keep Playlists when switching Apple ID?

So I have been using my moms Apple ID for years, all of our music has been on there since we started getting iPods and iPhones. Lately, it seems many of my pictures go to her devices. Whenever she tries to call my sisters phone number, I get called instead. I think it’s all due to complications in the cloud, but I don’t really care, I just made a new Apple ID so all of our things would stop getting intertwined. Once I made it, I lost all of my playlists. My mom added me to the family sharing thing so everything else was pretty much unaffected. However, i could not for the life of me find out how to get my playlists back to the way they were. We have Apple Music, and with family sharing I’m part of the same subscription, but I tried looking through iCloud settings, Music Settings, everything and nothing would get my playlists back. Eventually I just plugged my phone into her laptop because my playlists are all there, but when I tried to sync the music back to my phone only half of the songs would go through, I was getting an error message saying something like “songs from Apple Music Cannot be copied to a phone”. So what am I supposed to do? As of now I just switched back to my moms Apple ID to get my playlists back, but is there no way to have them using my new Apple ID with family sharing?