"We're a happy family
We're a happy family
We're a happy family
Me mom and daddy"
The Nuclear Family were a group of evil, stupid atomic-powered robots who fought Batman and The Outsiders. They were created by nuclear physicist/robotics expert Dr. Eric Shanner, who lost his family to the effects of radiation.
I guess Shanner forgot to wash his hands after he got off work at Los Alamos, because he gave his family a lethal dose of the Atomic Crud, which was pretty careless of him. Grief-stricken, the brilliant but hygienically challenged physicist did what any of us would do if we lost our entire family to radiation poisoning: he created creepy robotic replicas of his dead family. Oh, and he gave them all powers that replicated the effects of a nuclear blast. You know, to honor the memory of the deceased. Dr. Shanner also creates a replica of his younger self ("Dad") to interact with the rest of The Nuclear Family, which is weird. Plus, he creates a robotic version of the family dog. Shanner must have really loved that dog, although not enough to give the dog replicant an actual name - it is referred to as "Dog."
Batman and the Outsiders writer Mike Barr had a knack for creating stupid villains who were seemingly designed around their catchy names like The Nuclear Family, The Force of July, Masters of Disaster, Ghetto Blaster (no, really), and Agent Orange. The Nuclear Family represents the height of dumb villainy created solely as opponents for the second-string Outsiders. To my knowledge, they have never been used by any other writers on account of them being so damn stupid.
As you can see, The Nuclear Family are a caricature of the gee-whiz 1950's jet age whitebread American family and its uneasy balance between suburban domestic bliss and Cold War paranoia. A lot of the villains Barr created for Batman and The Outsiders were broadly satirical takes on American life (Duke of Oil, anyone?) and The Nuclear Family was no exception. I get the underlying metaphor of The Nuclear Family - it's not particularly subtle - but that doesn't mean I have to think they are cool.
Because they are not cool. The Nuclear Family are lame-ass villains and that's why they are here.