There will be people on here that will tell you that kids and chickens have mixed together for years. And while that is true, it often ignores the fact of space. A lot depends on the size of the yard.
A smaller yard, means a higher concentration of poop and the more likely that the kids are going to be in it. At the ages of your children, who still rather constantly put their hands in their mouth, I would recommend keeping them separate.
Also, if you have a rooster, the rooster is going to see this as his territory, and could very possibly attack the kids for playing in their yard.
Chickens are domesticated animals, that can live confined. Many people on here, think that if they free range in the backyard, they can have more chickens, but that really is not true, the coop size is a limiting factor, and with the winter, free range does not help that much, because they are roosted up in the long dark nights.
Mrs K