Terry and Pamela are engaging in what would technically be called adultery: she is married and has two kids. However, she is an abusive, dysfunctional relationship. She is so depressed that she is taking Prozac, has to work two jobs because her husband cannot hold a job, and to make things worse, he hurts everyone in the family. “We want to know what to do to make him go away,” they both ask.
Since he is the father of the children, it will be virtually impossible to make him go away completely, but she can get a divorce and ask for fully custody of children. I would say that rather than argue endlessly about banning him altogether, it is best to give him some visitation privileges. I think it will be best for children if they were not for too long with such an abusive father. In other words, your girlfriend needs a divorce attorney right away.
And once the divorce is final, you can become their new dad and start treating kids with love.