I'll probably have to call, because in both RCI and NCL I'm not allowed to put more than 2 kids, when 2 adults. Just checked.
Loads of ships have 5 berth or more cabins NCL have ships with cabins that hold 8 RCI has loads of 6 berth + look at navigator of the seas out of Southampton, the larger cabins hold 5 or more. They have a decent sized 1k grade 8500 and 8200 they hold 6.(min 4)
3 weeks are south of the Azores/Madeira. That is not wintery, especially so the Carribbean but there is a small chance that hurricanes could disrupt things this time of year.
Problem is that I never find one cabin for family of 5 except Disney cruise
19 days at sea out of 33? I dont think that's good especially with the sea at winter