M.L.
They are not hookworms. Hookworms do not come out in poop, only their microscopic eggs, the worms latch into the intestine. What you see are tapeworms. Hookworms (a type of roundworms) are almost impossible to see with the human eye, but the tapeworms are not. Roundworms can be seen in long sections, tapeworms will be little segments, like rice.
Fleas are what carries tapeworm, not hookworm. Hookworm is passed by accidentally ingesting larvae in the environment, through and infected mother's milk or puppies born with it, and larvae can actually crawl into human skin (eww).
Hookworm eggs/larvae can lie dormant for years in the ground. Tapeworms are not as harmful as hookworms, but hookworms can be dangerous to children and can cause anemia among other issues.
Even if you remove infected dog poop, the eggs can still be in the grass/yard.
You can collect a stool sample from your child to see if worms are present, you can take them to the pediatrician. Do not use any kind of cloth or paper towel to pick up or wrap the poop it as the fibers can mask and/or absorb the worms, just put it in a plastic bag. Info on what to look for if your child is infected and how to treat it here: I would call the nurses line just in case.
http://www.livestrong.com/article/206919-how-to-treat-tap...
Okay, I am grossing myself out. I have worked with animals a few years at a vet and emergency clinic and shelter as well and have seen some royally disgusting things. Hookworm infections can be very serious, tapeworms not as much.
http://www.dogbreedinfo.com/worms.htm
http://www.dr-dan.com/hookworm.htm
http://www.dog-health-guide.org/dogwormstypes.html