cyd, my son is 12 and I still worry.
I'd suggest that you choose a cabin without a private balcony. While the balcony doors are pretty heavy and even I find them hard to open at times, it may put your minds at ease if you select a larger oceanview cabin. You can all enjoy the outdoor decks together, with youngest child's hand in yours.
Which ships are you considering? And, how old are your kids? Many ships today have kids programs with lots of activities and safe places to exlore for the young ones.