I don't know whether the same person has to sign the child in and out of the Kid's Crew Program but I called NCL to ask if I needed to sign my grandaughter up in advance and they told me no, it's done when you get onto the ship. Hope this helps a little.
When you board the ship (at the kids club) you fill out forms for each child. A parent or guardian over the age of 18, who is on the form can sign the childin or out of the kids club. So.. one parent can sign in, the other out. If the counselor doesn't recognize the parent, they may request ID. Kids in the teen club, come and go as they please.