You've already gotten good advice about worming the chickens, but I just wanted to point out a few things. DE does nothing at all for internal parasites, ( and it is questionable regarding external parasites). DE "works" as an abrasive that damages the skin and dehydrates on soft bodied pests such as snails and grubs, that is why it is frequently used in gardens. It completely softens up when wet, so it literally can't do anything to worms in the intestines.
Secondly, chicken worms may not be a danger to your toddler, but dog worms are. You would not see worms, unless your dog is overloaded with them. A fecal test by your vet is best. If you have your dog on monthly heart worm protection, you are fine, that will get most intestinal worms as well.
Thirdly, hand sanitizer only kills bacteria, it will not kill or remove worm eggs. Washing with soap and water will do that. Just a little FYI.