Hi We sailed on the Ventura in May and children were allowed in all the bars and clubs,some of our fellow passangers seemed to pull their faces a bit when youngsters came in with their parents, I think they have forgotten they used to be young once.You will most likley find that with the the entertainment and clubs specificly for the ages you mentioned you won't see your teenagers until they come to tell you it is time for bed.
We've been on some of the other P&O ships in a crowd of a similar size and with children the same age as you've mentioned.
The children are allowed in the showbars and most of the other bars. The only bars that I seem to recall that they were not allowed into the more "traditional", quieter bars. These are in the main populated by the more senior cruise passengers. Also, I think that Disco is out of bounds.
Do bear in mind though that the 14+ children (I think), usually have their own Disco most nights in the Chidrens' Club area.
Have a great time!