I hate to say it, but a letter like that will only be an excuse for her to use. Addicts use any and every excuse they can.
Ultimatums to an addict are useless. The drug will always win.
I'm sorry you are going through this, but honestly, there is nothing you can say or do that will make her ready for recovery. Please take the time to read around this forum and also our Friends and Family forums. You are not alone. Welcome to SR.
Friends and Family of Substance Abusers - SoberRecovery : Alcoholism Drug Addiction Help and Information