It has been a long time since we cruised with our kid. Of course in the meantime we have observed many families with kids on many ships.
Here are MY suggestions:
#1 -- kids under 6 stay home with Grandma! You will like it better, the kids will like it better, and grandma will like it better. Kids 6 to 12 are in the optional class. You have to consider their behaviour and experiences.
#2 -- you have to give a lot of thought to your kid's dining habits. If their idea of going out to dinner is Mickey D's, let them say home with somebody who will take them to Mickey D's every night! They will like it better and so will you.
BUT -- if your kids, like ours, are accustomed to nice restaurants and able to sit through an hour and a half of dining and try new and interesting foods, then they will LOVE the MDR and share a family experience with you. So many times I have observed families in the MDR and felt impelled to go over afterwards and compliment the parents.
#3 -- The kids programs are great. Make sure they participate fully.
#4 -- Leave video games and cell phones home. Don't let them use the DVD in the cabin except for very special treats. Cruising is an old fashioned laid back lifestyle and there is no reason kids can't experience it too.
#5 -- Be sure they do their homework before the cruise. Every single port, whether it is St. Thomas or St. Petersburg, has a history and an important relation to trade. The more they know about the port in advance the more they can learn why they are there. Disguise the schooling as a vacation and they will love it.
#6 -- be sure they have a good lesson in elevator etiquette. On one cruise, we had two kids push past us and say, "Get out of our way, old farts." Well, lo and behold, a couple of days later the elevator doors opened and one of the kids got into the elevator with his parents! He froze up, refused to even look at us, and got to ride 6 floors in anticipation. As we left the elevator, I turned to him and said, "thank you, young man." I hope and trust his parents asked him what I was saying "thank you" for!!
#7 -- DON'T FORGET THE SUNBLOCK!