We've sailed on the Zaandam, Mercury, and Norwegian Sky and all 3 had terrific kids programs. Activities were seperated by age. My son who was 7-8-9 on the trips enjoyed them a lot and I could see that the younger kids were enjoying themselves as well.
Parents had to sign the little ones in and out of the kids rooms so you shouldn't have to worry about security either.
I would guess that Princess and RCCL are equally good.
Be sure to check out Princess and Royal Caribbean as well. We cruised Alaska on Celebrity Infinity and while there probibaly was a "kids" program, we went later in the season and hardly saw more than 2 kids the entire trip. When are you going?
Yes all the ships now have kids programs, but expect far fewer kids than compared to the Caribbean. With the kids that young, you may want to look into extended activities and sitting options??? I doubt you are going to want to consider costly touring that they may not be interested in? I strongly feel you get only half a trip without them, what seeing Alaska is all about.