WIMBLEDON, England—Coco Vandeweghe, who won her second-round match at Wimbledon on Wednesday, has a feisty confidence that’s ideal for a tennis player. She got it from wrestling as a kid growing up on Long Island.

The 23-year-old Vandeweghe comes from an athletic family. Her grandfather, Ernie, played for the New York Knicks. So did her uncle, Kiki. Her mother was an Olympic swimmer and volleyball player. Vandeweghe grew up playing many sports—including basketball, volleyball, squash and golf—and didn’t start playing tennis...