I'm not understanding why she needs to nurse at dropoff and pickup at all? Does she live that far that she can't wait until she gets home to nurse the baby? I can see a newborn maybe that would have to nurse often, but if it's a child that is old enough (I'm assuming a year or older) why can't she nurse in the morning and then when she gets home after?

That would a great inconvenience in my opinion. I mean, I never have had a mom ask to give a baby formula in a bottle at drop off and pick up, I definitely wouldn't let that happen, so I wouldn't with a nursing mom.