If i delete music from itunes, will it delete from the iphone?

My mom and i share an i tunes, but i have to sync her music too. I don't want that. If i delete the music listed on there, will it delete the music from her phone?

Most probably.

If you sync, yes. You do know you can change the sync settings of the phone to pick and choose what you want without having to delete the music. When you connect the phone and it shows the summary screen in that same row with the summary tab you'll see a music tab. You can change it to selected items and apply those changes.

When you sync, the song on your iPhone will erase.