I went on my first cruise this Summer with DS. I admit I assumed we would be spending all day every day together and didn't really investigate the adult only stuff before we went. On the very first day he went to the kids club and I knew then I was going to have 'Me' time. I lounged by the pool (for an hour one morning I was the only one there), read a book and had a shower (without interruptions, a rarity) and even went to bingo. Sadly I didn't go to Palo. I was planning to go to one of the solo lunches but got caught up in other things. We did lots of things together, games by the pool, mouseketeer, pin trading and swimming. When we discussed booking again I said maybe we wouldn't do formal night in the dining room, he said no, we had to go because he'd miss making friends.
Next year we are going again and I have no qualms about either of us having fun, travelling alone on a ship with him (totally safe), or keeping him occupied from morning to night. Although we spent money in the stores we didn't go overboard and I didn't feel the need to pay for extras like we have on other holidays. There was never any pressure to join in either.
I can also say I came back more relaxed than I ever have from a holiday. Your kids will have fun, you won't have to worry about them having fun or what to feed them and you'll make some wonderful memories.