I have heard of situations where there might have been a couple of families traveling together on World Cruises, but it's very rare. The family is gonna first of all need to be pretty well off to afford a World Cruise. Most World Cruisers are older folks who have already accumulated their nestegg. Families generally are still building it up and would be unlikely to be willing to dedicate the financial resources necessary to take the whole family on a World Cruise.
Secondly, and even more important, the World Cruise would involve pulling the kids out of school for an extended time ... or they would have to be home schooled children. While pulling the kids out of school and home schooling them during the cruise would be possible, it would be difficult. I did hear of a case a few years back, though, on Cunard where there were like three families onboard with their kids and they got the Hotel Manager to set up an area in the dining room for "school" each morning. Two of the families brought along a private tutor for the kids, while the third had one of the parents home schooling. But, again, this is rare.
I doubt you'll see any kids on the world cruise, to be honest ... be it on Princess or any other cruise line.