if a will only mentions 1 child but there are 2 other children not mentioned the will. does the law require all children be listed?

Usually a will will identify all those that are takers under the will.  When discussing children, it will say something to the effect of "all those born unto me", and then allow for any inheritance to be split among those takers.  If the will only mentions one child and doesn't have language to include other children not yet born when the will was made, those children may be out of luck.  However, any will can be challenged.