What I've learned on 10 cruises---
They TRY to meet requests. If you ask to dine with just your family, they make a real effort to do that.
If you don't ask, it goes by how their table arrangements work out. They have tables for 4 and up. We have been seated (just 2 of us) at a table alone. We were also seated with a group of 16 others, but they did ask us before they did this--it was a lovely family, and DD enjoyed being the "big sister."
On another occasion, we were seated with 3 other groups of 2 at a table for 8--all ladies/teen girls. Another time, it was a family of 3 with daughter about same age as mine.
It isn't random. They try to match kid ages as best they can (although the older ones sometimes get counted as adults. My DD was 12 when we were with a grandmother and 17 year old as well as 2 sets of adult sisters for a total of 8.
If you are seated with someone (other than your family) and it isn't working out, just tell the head server. He will have you moved for the rest of the cruise.
If you want to be with someone, the key is to have your ressies "linked." That's
DCL talk for "we want to eat together."