I was also going to recommend looking at NCL and the Haven category of cabin.

I have not been on that line, but understand from my TA that often times older clients of his like the Haven because they can bring multiple generations on one ship. The ship will have activities for the younger kids as well as private quieter areas for the older.

You get priority on/off the ship, their own pool (for everyone in Haven, not per cabin), private dining room etc.

Sometimes the older folks have gotten off their Silverseas or Seabourn cruise and then transfer to the NCL Haven and have the kids/grandkids join them.

Most importantly, why are you going? Are you going for the kids or for you? If you're going for the kids, do the Disney. It's very nice and the kids are a perfect age for that.