Panic in Year Zero! (1962), directed by Ray Milland.
On the first morning of their vacation a family notices strange flashes of light and then a mushroom cloud in the direction of Los Angeles. Yes, it's the Big One, world wide.
Dad (Ray Milland) soon shifts into rather ruthless survival mode, clearing out a grocery before the townspeople know what's up, robbing a hardware store at gunpoint and slugging a gas station attendant. He's not a savage, but family comes first and he's doing what everyone has to when civil society fails.
He spends a lot of time arguing with his wife (Jean Hagen) but the son (Frankie Avalon) is having a good time: carrying and using guns, crashing through road blocks. It's all matter-of-fact and realistic, the things you have to do at the end of the world as we know it: get supplies and guns, find a place away from other people, don't trust anyone. Perform executions as necessary.
The state of nature is particularly hard on the women: the daughter is raped and they later rescue a young woman kept as a sex slave after her family was murdered. Dad showed mercy to some thugs earlier and that turns out to have been a mistake.
The low budget production values don't hurt this at all, but there are problems:
Ray Milland's is the only vivid character. The rest of the family is bland.
The dutiful family is a bit TV-myth squeaky clean.
The main villains are hot-rodding juvenile delinquents, stock characters of the period.
In the second half much of the outdoors is actually soundstage, damaging the illusion of realism.
The jazz score would suit an urban police drama but is all wrong here.
On the same two-sided disc with The Last Man on Earth (1964).