Carlos - I am not a parent so what do I know about it, but I would do what you feel is right as a dad, not as a DBing LBS.
I am amazed at some of the similarities in the behavior of your W and my H. Mine avoids using my name in emails, too. It is very strange for him. In the first couple months, I assumed it was to show me he had no feelings for me. At some point I told him I accept our reality and he should feel free to address me by my name. He said he would. He still rarely uses my name. I now think it causes him pain. I really do.
Mine also looks like a ghost. But in my situation, no one who has known him long enough has seen him. He is artfully dodging my family who are trying to reach out to him. He is no dummy. Most of my family think I am exaggerating when I describe his appearance. Only one mutual friend, with whom he works, sees him and she recognizes the changes, but she sees him daily so it's less shocking.
But back to you. You are an amazing parent to your boys. You are teaching them both amazing things about love, understanding, compassion and kindness. I wish all parents were like you.
