What a sad, sad situation. Can you reimburse your neighbor for the baby goats? It won't replace them, but maybe you can offer to do chores this summer or something to try to repair your neighbor-relationship?

What kind of fence do you have now? Might cheap stockade-type fence, on the other side of the electric fence so she cannot "see" the goats or other animals, help?

A prey drive is nothing to mess with, I would definitely contact any behaviorists and see what they say.