Fetal hemoglobin v. mother's hemoglobin?

You're kind of answering your own question. Saying that fetal hemoglobin saturates at a lower partial pressure of oxygen is the same thing as saying that fetal hemoglobin has a higher affinity for oxygen. Think about what having a higher affinity means--it means that for any given partial pressure of oxygen, the fetal hemoglobin is going to bind more oxygen molecules. If you start with a low amount of oxygen and slowly ramp it up, the fetal hemoglobin will become saturated before the maternal hemoglobin.