mamaof4... I would still need to talk to at least ONE of the parents before releasing the kids. In an absolute emergency like this, I would let the kids leave with neighbor lady as soon as either mom or dad had verbally okay-ed it.
I would need to hear it from the parents directly, because as extreme as this could get; many, many abductions are perpetrated by people known to the family. That may be the absolute worst case scenario, but it could happen. And I wouldn't want to have any part in it.