We have been on 4 Disney cruises admittedly some years ago, so unsure if it’s changed, but we never found it an issue to have the children with us. We would have a drink, play bingo which they loved, dinner & show. Then a walk around the ship before bed around 10/11pm.
But I understand the European way as I am too (British Cypriot) & our children went everywhere with us. We didn’t really do kids clubs either.
We are in Cyprus at the moment & were out with family last night. The children were all running around having a blast till gone midnight.
Children are not hidden away here & that is a cultural difference. Mind you the U.K. that wouldn’t happen. So I understand the differences & just go with it.