D..
I'm so sorry about your little one, J.. What a bad break for all of you (no pun intended...)
That said, J., you just MUST make that child wear the sling. Talk to the doc about ways to discipline her to get this done. I'm sorry, but allowing her to call the shots here because of her behavior fighting you is a recipe for disaster - like surgery. Her collar bone will heal wrong and your daughter will be disfigured.
This isn't just about safety. This is about making her heal normally so that the rest of her life is not affected.
Forget about her strong need for independence. You must take the reins here and MAKE her do what is necessary. Period.