One of the rotations is adults sailing alone and older kids. It is usually the latest start time (as the above poster said.)
If you want to be seated alone, first call and make that request. Then after you board, go to "dining changes" and ask to be sure that you got what you requested. If not, again, ask to be changed. It can usually be arranged at this point.
We've been delighted with our seating arrangements. When DD was younger, we were frequently seated with a family with only one child, always a girl and always within a year or 2 of her age. As she became a teen, we are usually seated with adults or families with another single mom/teen combination (or grandmother/teen). Bottom line, if you don't like your dining companions after the first dinner, go to the head of the dining room and request a change. I've never heard of that request not being granted.