Husband had affair resulting in baby in another country?

my husband had an affair resulting in baby in another country while on business there for 6 months. From pictures, the favors our children and looks american. 4 years ago, I decided that I would stay and reconcile my marriage and mainly because we have 3 teens together and felt this would devastate them. (Our teens know about the affair, but not the baby).However, I just discovered emails from her and him from a few months ago and his conversation is clean, but hers is not. She refers to him as her "big bear", or uses words like "our beautiful son together". In other instances, she attempts to get him to agree to bringing the child here for education. - I approached my husband about this and he says he would like to be in the child's life. But he also shows signs of preparing for our life together after our teens leave. He's putting away retirement for us, he talks about us traveling together, and much more. But I am not sure where this child would fit into us if this woman continues to talk this way. By the way, he and I have both had conversations with her in regards to being respectful and she continues to do so. (PLEASE READ ALL AND ONLY CONSTRUCTIVE ADVICE IS WELCOME).