I would not share that letter with her. I think it imprudent to have threats of violence associated with you in writing.

I think it is good to discuss all of your feelings with her, including the fact that you would never hurt her.

I am very sorry that she made that invalidating comment, and for the profound hurt it caused.

That anger is worth thinking and talking about. It is understandable that you have it, and understanding it better will help you come to terms with what happened when you were growing up.