The internal conflict that exists at Updike's "Separating" rests with the struggle of Richard to do the right thing as he and his wife prepare to tell their children they will be separating.
Richard wanted to tell everyone at once, but Joan did not. Richard's conflict at the start is pretending that everything is just as it's always been—while it is totally untrue.
So he had drudged away, in love, in dread, repairing screens, getting the mowers sharpened, rolling and patching their new tennis court.
Richard is also conflicted by Joan's plan: to start with Judith and then tell the others. However, he feels that something is off with the plan:
...it had an edge of false order...like Joan's long chore lists...
It is inferred that there is something contrived in the telling—something less than forthright, and manipulative. In carrying it out, Richard also feels that it makes the separation that much harder for him:
Her plan turned one hurdle for him into four—four knife-sharp walls, each with a sheer blind drop on the other side.
The four hurdles are telling his four children separately. Richard is worried about how the children will cope. He works hard to prepare the house "against his absence." He hides the future that waits "vaguely" in front of him—for nothing seems certain, and he is unhappy about the need for what awaits them in the telling of their broken relationship. He fears the loss of members of his family because of the divorce.
As Richard continues his chores, his pain is evident. He...
...clumsily hammered and chiselled, each blow a kind of sob in Richard's ears.
As Richard faces his children, he is overcome with tears; he struggles to contain them—joking about his allergies. His love and his pain assault him.
The "third person" in the marriage is someone Richard has been seeing. Joan handles herself well. However, we do not learn of her inner-most feelings.
The children all take the news differently. Judith dismisses the idea of a trial separation: be married or be divorced! It is hard to sense what kind of internal conflict she may be experiencing. John gets angry and acts foolishly at the table. His inability to understand bursts forth, so the reader can assume that he is struggling with the news. Ultimately he pulls himself together and tells his parents that he's fine. Margaret is stunned by the news, but the narrator does not give a great deal of information regarding her feelings.
Richard tells Dickie—having picked him up from the train. At first this son seems unaffected. His lack of emotion upsets Richard, who sends Joan to check on him. Dickie's lack of "tantrum" makes Richard feel sick. When he at last goes in to check on the boy, Dickie still pretends that he is all right, but when Richard goes to kiss him goodnight, his son—with his face covered by tears—kisses his father and...
...moaned one word, the crucial, intelligent word: "Why?"
Dickie's pain is visible. Richard's pain is gut-wrenching as the reader finishes the story:
It was a whistle of wind in a crack, a knife thrust, a window thrown open on emptiness...Richard had forgotten why.
The use of images of knives throughout the story can only imply the extreme pain Richard is feeling, even while he tries to cover it up. For in face of all that he loves within his family, his reason for turning away from Joan is something, by comparison, that he can no longer even recall.