1) If you're writing your wife letters, you're not detached.
Give her some space. Let her see you during the times that you see each other, which sounds like it's when you see the kids. If you write her letters, you're pursuing.
Space is your friend here. It sounds counter-intuitive, but give it a try.
2) If you want to get back together with your wife, don't date other women, even casually. In a woman's eyes, "It didn't mean anything" doesn't hold much water. Dating other women does NOT show your wife that you want to get back together with her. I'd wait a while before dipping my toe in the dating pool if I were you.
As with all things, YMMV....(Your mileage may vary).
Good luck! Chin up! Hope you find some positive things in your day!!!
