Try NCL cruise line. They may have what you're looking for. They also have a fantastic kids club! We couldn't get our daughter out when we went to collect her! NCL are great!
Rachael Lewis-White, Derbyshir.
Navigator of the Seas and the new Independence of the Seas (RCCI) both have family rooms and inter connecting rooms.
Hope this help.
Try Costa as seem geared towards families. We were on Costa Fortuna and lots of Italian families with children aboard.
Island star have interconnecting rooms and a very friendly 'english' orientated ship. the costas have the same cabin types not so english more continental families, with the Island ships all your gratuities are included not so with other ships, read all the small prints for extras not included. You can sleep with you interconnecting doors ajar if need to.
I know that some Celebrity ships have family rooms but they do sell out quickly. Many of the Carnival ships have inter connecting rooms which are generally cheaper and there are more of them.
P&O ships have connecting doors, or the mini-suites are big enough to accomodate you all.
All get booked up v early though, so you have to be quic.
Royal caribbean and NCL both have cabins for families, both with very good child facilities.
Princess cruises will accommodate children, you can have connecting suites, and they have childrens clubs for the small children right up to teenagers.
We have booked two connecting outside cabins with RCI on Mariner of the Seas. Booked a fly drive holiday and then the cruise separately as it was much cheaper. Each cabin costs £600 approx for the week in October which I think is excellent value. At £85 a night for each cabin including meals and entertainment, I would be hard pushed to get all that at a hotel in the UK. The plus side of having two cabins, is two separate toilet/showers and some peace and quiet for Mum and Dad. Good luck with your search.