Doggie wee should not be a problem with humans, but dog poo on grass can be more serious as it can transmit parasites into the grass, which very very rarely can cause harm, in that it can cause blindness.
I have bred and shown dogs for many years, and also been a dog host.
Meanwhile, I do not wish to cause scare and upset. Breeders normally keep dogs in runs so that they can be scrubbed daily with a disinfectant such as Jeyes Fluid.
It is question of simple hygiene really, after the garden a good wash of hands and face will do the trick. Maybe your son could section off a dog free area for the children to play in.
Again sorry to be the bearer of this news, but it has to be kept in perspective. Most people I know have dogs, chick, ducks, horses etc, and children or grandchildren and just get on with life. I am sure all will be ok. Mrs Bouquet