Actually sometimes, it's true that both Dexter and Carolina are actually trying to be good parents to Antonio, even though it's possible that Antonio is trying to be a child who doesn't fuss, or also cries when he's sad.
Carolina understood her son's attitude. But in fact Antonio is a bit similar to Immanuel in character. But indeed Immanuel never wanted to come to see Dexter to New York, nor did he want to come to tell him that he was Dexter's son.
For some reason, Antonio was able to understand Dexter's feelings better, his father. Even if Dexter really hoped that Immanuel would come and see him in New York.
Actually, Dexter knew that maybe his life with Stella would never be united by a love relationship. But indeed he also knew that for example Stella was a woman who actually really cared about her son, Immanuel.