In John Updike's "Separating," the external conflicts are seen between the members of the family as Richard and Joan prepare to tell their children of—and then discuss—what they say will be a trial separation.

There are two kinds of conflict: internal and external. 

Conflict is the engine that drives a plot.

Conflict exists here between characters. In this story, the external conflict seen is man vs. man.

The first conflict is between Richard and Joan. The narrator infers that Richard has had an affair. It is not something that gives him joy—her presence is "vaguely" presented to the reader, and seems equally vague to Richard. They tell the kids they have grown apart, but the truth must cause Joan a great deal of pain. The narrator does not give the reader any deep insight to what she is feeling, other than through her conversation with Richard—the chasm between them is obvious.

It is Joan that comes up with a plan to tell the children separately. However, like ripping off a band-aid, Richard wants it to be over quickly—telling them all at the same time. 

Her plan turned one hurdle for him into four—four knife-sharp walls, each with a sheer blind drop on the other side.

Rather than saying it once, he must carry out the telling four different times. Richard agrees to Joan's plan, but Joan senses some criticism from him and becomes sarcastic—exposing the conflict that exists between them as their marriage comes to an end:

Do you have any better plan? That leaves you the rest of Saturday to answer any questions, pack, and make your wonderful departure.

The lock Richard fixes on the door may be symbolic of the opening of a closed portal that has hidden their secret. Richard cannot keep from crying at dinner. As the children clear the table and go into the kitchen, Margaret asks why "Daddy" is crying. Judith (who was told earlier and asked to say nothing) tells Margaret and John. Suddenly, Joan's plan falls apart.

There is some sense of conflict with Judith—emotionally calm, she dismisses their idea of separation. She believes they should be married or get a divorce: nothing in-between. Of the children at the table, John is the one who reacts most forcefully. He becomes angry, demanding to know why they had never told the children they were having problems. Then he begins to act foolishly, and Judith tells him to grow up. 

The conflict that is shown in these examples centers around the separation: it rises up between Richard and Joan, between them and the children, and—on a smaller scale—even between the children—something Richard had feared.

Conflict between Richard and Joan appears again after dinner. He apologizes for crying:

I couldn't stop. I wanted to but couldn't.

Joan is accusatory, saying he did it on purpose:

You didn't want to. You loved it. You were having your way, making a general announcement.

Joan sees his crying as Richard's desire to tell everyone at once, even though she had planned to tell each child separately. She thinks he purposely sabotaged her efforts.

Joan reminds him:

You still have Dickie to do...

Richard notes that she also implies, "That's one piece of your dirty work I won't do for you."

Dickie is, in fact, the child who is hardest to tell. He tries to act unaffected. This conflict comes from Richard's inability to explain to his son "why." There is no aggression here: simply two people trying to connect—looking for meaning and comfort where there is none.