My oldest daughter, Josey, had had low platelet counts since she was born, but the doctors always said it was nothing serious. When Josey was 7 years old, though, I noticed her bruising from gymnastics had gotten much worse, and she was more tired than usual. So I had her blood counts checked again.

The bloodwork showed more abnormalities, so I pushed the doctors to figure out what was going on. After a bone marrow biopsy, we learned...