After the break up she's seeing someone. Move on?

Well I believe this is my last questions regarding the subject. but here goes. My son's mother broke up with me a month ago. Now she's talking to another guy, he is already putting on her Facebook wall "i adore you etc etc" and she flirts with him as well. Anyway we have a son together and I had tried to keep our family together and tried to talk about things like adults. But she just has none of it. When I ignore her and become kind of a d***, she starts trying to reach out again. Now I'm 28 I don't like playing games or any of that bullsh*t, So I just wrote her a letter and said "I want to make it clear to you, right now I don't want to be with you. Obviously we have issues and that's why. I would be perfectly happy if we never got back together. What I want is to get to a place in our relationship were we can have a healthy relationship and be civil and respectful towards each other. I feel the best way to get to that is being apart and giving each other time. Time to heal and time to mature. What I hope for is once enough time has passed and we reached that point, we would be able to be happy whether were together or not. At that point, Because you are the mother of my son id still be open to the possibility of reuniting our family. But I think we are very far from that point right now. That is as clear as I can make it for you. I apologize for today but you were just being so negative and I'm just trying to tell you I want the same thing right now. Which is not be together, for those reasons. I hope you understand me now. Have a good day." So now she texted me and said she read my letter and I told her OK, and that I respect her choice and that's it. Now what do you guys think? Am I stupid for continuing to try? Be real and honest don't sugar coat it. Also if I just ignore her will she probably come around. Am I going to have to play this stupid little game. She' younger than me "24" I'm 28 and I just prefer to be direct. Anyway Thanks
Updates:
+1 y
we spoke last night. I told her I want to do what's best for our son and get along. She agreed and said she was talking to this guy. I said its fine and I wish her the best. We talked about past issues and mistakes and told her I just want us to have some space and time to heal. She seemed to get sad and cried a bit, but tried to not let it show. We then said goodnight.(best talk we had since breakup). After some time and space I would like to save my family..Do you guys think there is hope?
After the break up she's seeing someone. Move on?
3
3
Add Opinion