Don't know much about the kids program on HAL. I do know that Princess has a very good children's program.
If thinking about Alaska I would highly recommend picking a cruise that goes into Glacier Bay National Park.
Enjoy your cruise.
With integrity nothing else matters; without it nothing else matters.
We took our kids (S20 & D11) on a cruise to Alaska in 2005 and we were on Celebrity. Knowing that Celebrity caters to the more mature crowd we were told by our TA that in July there would be kids on board, so we took a chance.
If I had to do it over I would choose Royal Caribbean or Carnival because there was not a lot for them to do, but they still had a blast.