Most greyhounds are very tolerant of small children. As with any dog, play should be supervised and the child should not be permitted to abuse the dog. Normally a greyhound that is being abused will walk away. In rare instances they have been known to snap at the child. Greyhounds and cats .
Most greyhounds are fine with cats.
Be sure the adoption agency knows you have cats. They will be happy to introduce you to cat-friendly dogs. As a precaution, the greyhound should be muzzled for the first few days he's home. Once he realizes the cats are part of the family, there should be no trouble. Many greyhounds are actually afraid of cats.