Remove music from my iPhone
So it sounds like the music is on your iPhone and no other devices?  How does your daughter access music if it is not on her device?

If you have the music saved to your daughters device, then it should not matter if you delete it off of your phone.

For example, most of my music is on my MacBook Pro - I can add or delete music from my phone at will but that does not mean I lost my music because it is still on my MacBook.  I can listen to anything that is on my phone, or, with Internet connection, I can listen to anything I may have on the cloud as well.

This is my understanding, anyway.