Dog was having what he thought was a personal conversation with his son. He used a vulgar term, to his son, to describe a person he felt was hurting his son. The term was not directed at the woman herself, and therefore Dog owes neither her nor anyone else any apology. The
personal conversation that Dog had with his son was nobody's business. The fact that the son sold the tape and made it everyone's business is not Dog's fault nor should Dog be forced to take grief for what he thought was a conversation between him and his son.
Dog also had a right to expect some degree of loyalty from his son which he did not get. If I were Dog, I would tell the kid no problem, you're on your own, and when your girlfriend gets done using you and kicks you to the curb, don't come crying to me.
Sounds like the kid needs to be reminded which side his bread is buttered on.