Hi LisaM, welcome to Cruise-Chat! You know your children the best. If they get car sick, there is a chance they would get sea sick. There are natural remedies, green apples and ginger are two I know of. However, with as much fun as they will be having, I doubt sea sickness will be on their minds.
Like I said before, you know your children. I doubt that once they're on board, there will be much of a problem. How about flying? How about excursions? Can they handle rides in buses? Can they handle crowds? Personally, I think travel is the best education a child can receive. Disney is a fantastic line and offers a wonderful experience, not only for the children. I've been on cruises with children of all ages. Some of them love it, some of them throw tantrums.