Is this how I should leave my wife?

Well, it's difficult for someone outside of your situation to know what to do because we don't know how you wife acts/reacts like you do. I don't think it sounds like what you're doing is wrong. That's about all I can say. I guess just ask yourself how she'll take not only what you have to communicate to her, but the way in which you're communicating it (i.e. the letter). Ask yourself if there's a better way to go about it. If not, that's all you can do.