Is it proper for a nursing mom to nurse her baby at the table in front of nine other diners?

I agree with you 100%. Not everyone wants to see someone feeding - especially at the dinner table. The polite thing to do would have been for the woman to excuse herself and nurse the baby in private. Kudos to you for letting this woman know it was not appropriate! Obviously the woman had never heard of pumping milk into a bottle for such an occasion.