I personally would consider "high risk" for OB anesthesia any patient who was a clear undebatable ASA 3 pre-pregnancy, based on pre-existing medical disease, or is an ASA 4 now, due to pregnancy-related complications, or any difficult airway (beyond the usual airway edema - e.g morbid obesity, achondroplasia, cervical fusion etc.) or predictably difficult C-section. This might not be comprehensive, but it's a starting point. I would also add to this the patients the anesthesia staff is just not comfortable anesthetizing, like surgically-repaired and well-compensated congenital heart disease in the mother, but with a special physiology etc.
None of these belong to a limited resource OR or labor floor. It also seems that you have to consider the neonatal risk, since you don't have a NICU or peds, which basically rules out any preterm labor, or predictably complicated labor or delivery (pre-eclampsia or worse, cocaine use, alcoholic mothers, IUGR, placental pathology etc.). I am honestly shocked that they allow you to have deliveries without a few neonatal (ICU) beds and around-the-clock in-house neonatologist. It's a recipe for disaster. Even babies from healthy mothers and uncomplicated pregnancies can get in trouble occasionally.