We took our 3 grandchildren (with their parents) on the Alaska Radisson cruise in June and it was a marvelous vacation. The children - ages 4.5, 7 and 9 - loved it and the children's program was great. They only participated in it when we were on the ship and thoroughly enjoyed the many excursions. We did take turns doing shore excursions that would appeal to children. They loved room service - were no trouble in the dining room and were catered to by all the staff. I thought it a perfect family vacation.
I will admit we had 5 adults in the group so it was easy to take turns doing kids stuff. There are really no baby sitters aboard so they need to be able and willing to stay in the children's program if you want any time alone. Five is the minimum age for the childrens program but they had no problem with our 4.5 yr. old - because her sisters were there. I will admit the older the better, but this was a birthday cruise so we just did it.
Good luck