They watched the TV show as children in the 1950’s. I read it in a science fiction magazine in the last 15 years. It was in either Asimov's, Fantasy and Science Fiction, or Analog. They saw only a limited number of shows and it had an “alien” host. They never met anyone else who saw the show. The sister spent her lifetime attempting to discover the history of the show and only occasionally discovered a small piece of evidence. In the end she never did discover anything about it. The implication was that it was not a TV show but really a transmission from an alien.
I found it in the September 1998 issue of Fantasy and Science Fiction. It is "Mr. Goober's Show" by Howard Waldrop. The intro to the story by the FSF editors say it was originally published in "Omni Online" shortly before it ceased publication. Thanks to everyone for looking.