Hello ! Well I've contacted Apple Support but they told me to get in touch with Tech Support and I just gave up, especially since I'm 90% certain what I did worked. Apple Music works just fine, for both me and my family members, I can still get both free and paid apps for myself using my credit card, and I've tried the App Store from my mother's phone to see which account would be used and it was using hers for both paid and free apps. I didn't actually go through with a purchase from her phone, hence the 90%, but any transaction was going through her account and there was no mention of mine or Family Sharing so I think it's ok.
How I did it: When I set up Family Sharing and the Apple Music account I was doing it from a Mac. It forced me to turn purchase sharing on and use my payment method for all purchases of the whole family and there was no option to turn it off from there. I guess there are fewer options on the iCloud settings on a Mac. However, from an iOS device you can go to Settings -> Apple ID (your name) -> Family Sharing -> Stop Family Purchase Sharing . There is also an option to just tick off "Share my purchases", but all that will do is just stop other family members from accessing the apps, music or books you've purchased, but it still allows them to make their own purchases using your payment method. What you need to do is press the blue option Stop Family Purchase Sharing on the bottom of the page, this way it stops it completely and their purchases should go through their account once more.
I hope this helps !
