This season, Skate America is the fifth of six Grand Prix stops from Nov. 14-16. The Grand Prix season starts in France from Oct. 17-19, then moves to China, Canada and Japan before Skate America.

Each bead, each seam and every late-night whirr of her mother’s sewing machine travels with Kim Chae-yeon onto the ice. While most figure skaters dazzle in designer gowns, the 18-year-old spins in ...