We just returned from a 4 day in early March '04. We booked at the last minute, so we ended up with late seating - our kids (4 and 7) are early-to-bed kids, so the late seating was not our first choice. We put our name on the wait list at guest services, but were told it is difficult to switch because early seating is very popular.
We decided to just go to dinner at the early seating, and ask if there were any openings. The manager was more than happy to seat us, and told us that there are always people opting to eat at Palo's (adult resturant) on any given night, so there is almost always an open table.
Further, he said that most people don't go through the formal wait list to get reseated, but simply ask him or the other resturant managers - so they are the ones who know what tables are open and how they can make it happen. He was able to permantly switch us. Can't gurantee that this will work for you, but it worked out well for us.
I would strongly recommend that you attend as many meals as you can. The servers go out of their way to make things fun for the kids (magic tricks, jokes, etc.), and this is a very memorable part of the cruise.