(this is Randytenn's wife, Kim, by the way!)
On our park/cruise combo in Sept. 2000, we were both shocked to be seasick the first night of the cruise. You see, we are avid roller coaster fans and just came from WDW riding Rock'n'Roller Coaster and Tower of Terror (which we LOVED), so we didn't dream we'd be bothered by the motion of the boat. And we didn't bring anything, either!!
So we missed the welcome party on-deck because we were laying down, miserable. My dizzyness was just as bad laying down as standing up, and the noise of the hangers clanging in the closet as I felt every little movement of the ship made me nuts!! To top it off, we were both coming down with colds from too-cold air conditioning in park hotel. We should have turned it down. I guess I should have thought about bringing some medicine since I do get car sick reading while DH is driving, but I just didn't connect car sickness with sea sickness. Oh well, live and learn.
Then we got ready for dinner, even though neither of us felt like eating. I figured we might feel better if we tried to get up and enjoy the ship, and it did help a little, but I still felt really dizzy and a little queasy.
So at dinner, I explained our predicament to our server at Animator's Palate, and he was really helpful (Neil on the Wonder). He suggested to go ahead and eat a little something for dinner, not a lot, then go get some medicine from the front desk and lay down for the evening. Apparently, most people make the mistake of eating nothing, which makes sense, but he said it really does help to eat. And trust me, it did! So if the little ones get sick, maybe try to get something on their stomach first and then give them the meds. But it was so nice that the cruise line had medicine for free on the ship. I just wasn't expecting that. I don't know if that's common on other cruise lines, but leave it to Disney to be so helpful.
And, luckily, we only had this problem the first night. After that, we just had our summer colds to deal with, but even with a cold, the cruise was fabulous!!! Didn't have to take any meds after the first night, which was great.
Hope this helps you. Enjoy your trip!
Kim