It is certainly possible that a man would do this if he lacks the necessary emotional abilities to see beyond himself and see that he is hurting his family. And it does not sound like your husband understands, or at least he refuses to understand. that he is hurting all of you.
He would have to address his issues (whatever is causing him to act as he does) before he would be able to treat you and your sons with any type of decency. And that this point, he doesn't seem to have any insight at all. So the decision to keep seeing him is up to you. He will most likely not change how he is so it unfortunately leaves the decision making about the relationship up to you.