If she’s not disabled from it I don’t see how it’s worth much to a lawyer. Sounds like you caught the problem and are fixing it. Would there really be that big of difference if you immobilized the arm immediately vs waiting a week?

You could start with just asking the hospital how they missed it. It might not have been visible on the X-ray. And if she had continued pain, getting a second X-ray makes sense.

I just don’t get why you want to sue for this. She fell and broke her arm. There’s no guarantee she’ll be 100% again.