Kids will be 7 & 4.5 so quite young. There are loads of activities for kids' though from what I've read, including this dining scheme where they come and take your kids away after 40 mins.
But overall they will need to be looked after constantly. Their climbing abilities and the notion of being on a ship are not a good mix.
The ship apparently also has child minding/babysitting services, I wonder what the charges are like per hour for that. Might be another option for us to explore.