OIN,

Sounds like a really bad day. You need to give her space. As for the letter, I think it is too long. She is not likely to want to hear all of that right now. But you should say something. I think it would be good to tell her that you are sorry you spoke rashly (or use your words) yesterday. You just want the two of you to get along. And you will do your best to get along with her. And then close your mouth. Maybe when things cool off and tempers fade, you could give her the letter. But things are too stirred up right now.