The child must learn that while the dog is sleeping it is off limits. Any dog will eventually snap or bite if put in this situation. Parents must teach the child to respect the dog. For example, if the child is about to crawl onto the sleeping dog's bed, the parent must react the same way she would if the child were about to touch a hot stove or run into the street, fast and firm. Children and Greyhounds can live together peacefully if taught well.
Greyhounds are sighthounds.
They have been bred to chase. A hunting dog runs, catches and kills. They don't wait for the human to come and kill for them. This sounds awful, but it is an extremely important trait for people to understand. Some get along with cats and some do not.