Black Prince does not usually take children as there are no facilities for them on this small ship. I think children would also find the 4 different dress codes on this ship a bit tiresome, formal nights, informal nights (but still quite formal) Elegant casual and Casual night. As adults we did. Dress smart for the restaurant, yes. But the dress codes were a bit above themselves.
Black Prince is not ideal for children, however Black Watch, Boudicca, Braemar (and I'm sure Balmoral will be) are fabulous I take my daughter on every year.
There's usually about 80 children on board (up to the age of 16) BW872 would probably be better for you.