Shin splints probably aren't genetic, or passed down from parent to child. The most common risk factors include overuse, poor physical condition, competitive running, female gender, smoking, being flatfooted, and previous injury.
Other risk factors are double heel strikes in ballet dancers, low calcium intake among female athletes, increasing training intensity, and the use of worn shoes on hard surfaces.
If any of your children develop problems, see an orthopedic doctor or podiatrist who specializes in this area. Early treatment can prevent serious injuries.