PhysDoc,
Our prayers are with your daughter. When he was young, my son was stung by a Brown Recluse Spider, resulting in a spot similar to the one you described. The venom causes a type of blood poisoning that can't be effectively treated by home remedies; you and your wife did the correct and loving thing, taking her to the hospital. I know there is nothing worse than having a child( or grand child) in pain or sick and you can't do anything about it yourself. So, today is the day to be thankful for the people and Hospitals like Children's Mercy, Shriner's, and Saint Jude's; who sacrifice their own holidays to take care of our children. You can rest assured, your daughter will be well taken of, and will heal.
Mike