Keiko has a new tank in Oregon and a dream team of experts that gets him into shape. But soon they start fighting over what a realistic future looks like for this golden retriever of an orca.

After the movie “Free Willy” became a hit, word got out that the star of the film, a killer whale named Keiko, was sick and living in a tiny pool at a Mexican amusement park. Fans were outraged and pleaded for his release. “The Good Whale” tells the story of the wildly ambitious science...