Getting rid of icloud music (not just hiding it)

Question

so, I just bought a new car with Bluetooth music capabilities. I was very excited to have a small selection of music to be able to select from, and I actually added music to my phone for the first time. My issue, is that on the car's screen, I am seeing all the music I had purchased from icloud previously. I would like to remove these, but I cannot figure out how. These songs showing up are not on my phone, and are not on my itunes library.
what I have tried:
i have done everything I can to hide t he music. I've switched the selection on iTunes and AppStore to not show all music. When I look at my library on the phone, it only has what I had added. The things NOT on the phone are still showing in my car.
i went onto iTunes on my computer, and clicked on the little x to hide all the things that had been purchased. This works on the iTunes Store, but the items still appear when pairing the phone to the car.
the one thing I haven't done yet is sign out from iTunes on the phone, which I have read works. I feel there should be a better way to do it though. it seems this would only be a temporary solution, because as soon as I sign in again, the music would come back.
If anyone has a way to get rid of this music, it would be very much appreciated.

Answer 1

I don't claim bigger insight into how apples servers work but if I were to make iCloud music then rather then having a copy of each music number to give people who buy it and then store the very same data for every single one of users who bought it then I would keep the data 1 place and handle iCloud music streaming by controlling who could access the 1 place the music file was stored if that was the case then if you deleted it it would be gone for everybody forever