First of all, the eggs themselves have only a 1 in 20,000 chance of carrying salmonella, according to the American Egg Board. That's a 0.005% chance of one of our eggs giving us the bacteria.
A bigger concern for me is our hen's manure. After all, the birds don't use a litter box; they poop wherever they happen to be standing or sitting. For this reason, we have a strict policy of using sanitizer after handling the hens or dealing with their run or hen house in any way. We keep a container of hand sanitizer right next to the chicken coop to help facilitate this, and already both my children (6 and 2) know and follow the rule.
What about manure on the ground, from when the hens free-range? Well, they don't leave much manure behind. I've never yet noticed where they've pooped outside of their house or coop. I figure it's no worse than having wild birds landing their droppings in our yard. I just try to be sure my children wash their hands after being outdoors - and especially before they eat.
I also tend to look at things historically: Kids and chickens have been around each other for thousands of years. Before the 20th century, the vast majority of families had chickens - and it was often the kid's' job to care for them. This was also before people washed their hands much.
Finally, it's important to remember our hens are well cared for. They aren't over-crowded (like commercially raised egg layers) and we clean their house regularly. I don't think they are any worse than a cat who uses the liter box, then walks around the house, or a dog who eats (or plays in) his own droppings.