Hypothetically if a couple were to get married and had kids could they then between themselves make up a written agreement at the beginning of their marrige stating that "if one of them is caught being unfaithful the kids go to the other parent" well then say they get divorced and go through court can the written agreement come into play??

I guess you might say that is a prenuptial agreement and is binding in court. I don't know why anyone would involve children that way, seems to be a dirty trick, per se.