What pesticides are safe on the lawn if I have young children?

Organic. There are natural options when it comes to pest control for lawns and outdoor spaces. Consult an organic or chemical-free landscaper and use essential-oil based products when possible. Remember, dandelions aren't neurotoxic (from normal environmental exposure) but pesticides can be.
Organic. Approved organic lawn care products are made without the use of toxic synthetic pesticides. Ecosmart (www.Ecosmart.Com) is one brand specifically tested for safety around children and pets. I've used their stuff personally and have no affiliation with them of any kind.