"You would think that a father who didn't have contact with his children, if he wanted those children, he would toe the line a little bit," she said.My first reading of this was that she was saying that if he wanted to see his children he was going to have to toe the line. On rereading it I'm less certain of my interpretation, but the insinuation is certainly there. For the sake of this discussion, I'm going with my initial interpretation.
My reaction was, "How dare she?" The underlying implication are that they're her kids rather than their kids, and that she should have some ultimate authority as to what involvement he has in their life. To me it seems almost equally valid for him to say, "If you want to see the kids again, you have to let me have this affair." The world would explode if he did that, though, while her statement goes by with little notice.