“You know, that’s a great question,” Ms. Palin said. “And it’s lovely to think that he would ever even consider such a thing.”

Image Ms. Palin on the show. Credit... ABC

She added: “He is a part of the family, and you want to bring him in the fold and kind of under your wing. And he needs that too, Oprah.”

There was more: “I think he needs to know that he is loved, and he has the most beautiful child, and this can all work out for good. It really can. We don’t have to keep going down this road of controversy and drama all the time. We’re not really into the drama. We don’t really like that.”

Finally Ms. Winfrey cut to the chase, asking, “Does that mean yes, he is coming, or no, he is not?” (Pressed, Ms. Palin said she would extend the invitation.)

Ms. Palin is obviously hurt and angry about the way Mr. Johnston has exploited his connections to convert fame into fortune, but there are other reasons for resentment. In the age of balloon dads and transformative reality television Ms. Palin has emerged as quintessentially American, in terms of the America of the moment. Her career gyrations, life and family continue to feed a spotlight-hungry media carnival. In some ways her almost son-in-law’s quick and callous cashing-in looks like a junior version of her own quickie book campaign.

The title of Ms. Palin’s book is “Going Rogue,” but her appearance on “The Oprah Winfrey Show” mostly showed a politician-celebrity going for broke.