I have been reading and posting on this board since 2000 and I don't think that I have ever read any post that said it rained ALL week, maybe a day or two here and there but not the entire trip.
Upon boarding, go to the location listed in the Navigator and try and get your seating changed to early - don't get your hopes up but it does happen. You didn't say where you were from so if you are west cost and sailing out of Florida the time difference sort of takes some of the pressure off.
As far as surviving dinner, take my comments as suggestions and observations, nothing personal here. I guess the biggest thing is to be prepared - late dinner means 8:45 or so before you actually have a plate in front of you. Guess some depends on how regimented your children are - mine didn't know what schedule meant (still don't but they are 16, 22 & 24). How well your your children roll with the punches? Maybe you could work your way up to that at home changing your dinner hour a bit later each evening. I guess I would just be sure to talk with them before leaving and warn them what is going to happen. There is plenty to eat on the ship to get you through to dinner so that part isn't too much of an issue.
Good luck