All of the major cruise lines offer some interconnecting cabins, and all will allow kids to stay in their own cabin (though some will place the kids with parents on the manifest, and then switch the keys to set them up for the kids room at check in .... which is really silly imho).
We've cruised with our boys when they were under 12, and did have a seperate cabin for the boys, though we had a balcony cabin, with the boys inside across the hall. And, of course, we had a key to the boys room,
For a multi-generational group I'd recommend RCI, Carnival, or NCL for the broadest spectrum of activities.... something for everyone.
FYI our boys actually still refer to Alaska as their favorite cruise, above the cruises we took them on to the Caribbean, so Alaska is a good choice.
Thanks Kuki for some sound 'place to start looking' advice. Those were the very lines we first thought of -- I wonder if a dangling preposition is as serious a problem as would be a dangling anchor!
We'd thought perhaps of a window for the parents, with children in an inside cabin across the aisle. And from what you observed, as long as the correct number of people are sleeping in a cabin each night all would be OK.
Of course we have 'perfect' grandchildren who could be counted on to behave in a cabin.
None of our adult children have ever cruised. We really only came to cruising upon retirement.