Even if your biggest problem was being too detached, you still need to detach now. Being detached will allow you to make the best decision to heal yourself and to save your marriage. If you want to do one thing to show that you are still dedicated to your marriage, keep wearing your wedding ring. If she wants to reconcile, that will be enough of a signal. Beyond that, everything is pursuit and it won't work. For me, dropping all pursuit is the only thing that has had an impact on my wife's mindset and even then only a minimal impact.
Also, the email says "we were not the main priority." That means that she feels like the kids weren't your main priority. Make them your biggest priority by far and stick to it. Your wife will see that change.
