I think this is "Who Shall Dwell", a short story by H.C Neal. It was originally published in Playboy in 1962, and later appeared in a few anthologies.

As noted, the plot initially is similar to the of "The Shelter", the episode of the Twilight Zone, but the conclusion is much more optimistic. Exactly as the OP recalled, a mob surrounds a family's nuclear shelter demanding entrance. A woman begs "Even if you don't let me in, please take my baby, my little girl." The mother of the family gets up quickly, and before anyone can stop her, dashes out of the shelter, and her place is taken by a three-year old girl. With just minutes to go, the father also goes outside so that two other children can take his place, and he stands next to his wife to hold her hand as they wait for the atom bombs to hit.

In a final twist, it is revealed that the town is actually in Russia, and the atom bombs are the USA's retaliation for a first-strike - no clues had been given to that point, so the reader might lazily assume the family was a typical American one. P.K. Dick regarded this short story as "one of the finest our field has produced" (The Selected Letters of Philip K. Dick Volume One). The text of the story can be read at James Harris' blog (hopefully without breaking copyright).

I think this is "Who Shall Dwell", a short story by H.C Neal. It was originally published in Playboy in 1962, and later appeared in a few anthologies.

As noted, the plot initially is similar to the of "The Shelter", the episode of the Twilight Zone, but the conclusion is much more optimistic. Exactly as the OP recalled, a mob surrounds a family's nuclear shelter demanding entrance. A woman begs "Even if you don't let me in, please take my baby, my little girl." The mother of the family gets up quickly, and before anyone can stop her, dashes out of the shelter, and her place is taken by a three-year old girl. With just minutes to go, the father also goes outside so that two other children can take his place, and he stands next to his wife to hold her hand as they wait for the atom bombs to hit.

In a final twist, it is revealed that the town is actually in Russia, and the atom bombs are the USA's retaliation for a first-strike - no clues had been given to that point, so the reader might lazily assume the family was a typical American one. P.K. Dick regarded this short story as "one of the finest our field has produced" (The Selected Letters of Philip K. Dick Volume One). The text of the story can be read at James Harris' blog (hopefully without breaking copyright).