Your children can go at any time they wish during operational hours. Which are roughly 9:00 am to midnight, and sometimes 1:00 am... On the first day you are given a navigator as to what activities will be done at what times during the cruise. My kids now pick and choose what they want to do, but usually do more anyway. The only time they ask you not to sign them in is during transition, and this is when they are moving the children around from one activity to another. Ex. the may be at a movie from 2:00-3:00 pm. and they ask you to either sign them in after 2:15 or after 3:00 back where they will be when it is over.
The kids can go for supper with the kids club to the buffet if they wish. You are also issued a pager, and when they have had enough, you will be paged, with the exact location to pick them up..
HTH