I feel the pain, in your letter I am sorry your hurting so bad I agree the letter will not work even if she is sober when you give it to her. We can not love the addict enough to make them stop even if they wanna stop addiction is very powerful stuff.
You didn't cause it
You can't cure it
You can't control it.
Your caught in the manipulation dance and that never works.
What does work well your mom has to hit her rock bottom when or how that will happen only her HP knows but you can save YOU maybe attend some meetings for you?