Just came back from Disney Dream, same size ship as Fantasy. I am very prone to motion sickness and especially sea sickness. I have tried the seabands/acupuncture before on a smaller ship (Celebrity Xpedition)in the Galapagos (good weather so relatively calm seas) and that did nothing at all to keep me from turning green within 5 min of boarding. Only the scopolamine patch for behind the ear has worked reliably for me, which is what I brought. I've worn the patch aboard a catamaran in the wintertime on the open seas around Hawaii and it really helps minimize the seasickness there, where the waves can get very choppy.
For this cruise, I had the patch with me. I did not put my patch on immediately because I find it severely interferes with my palate (I believe it dries out your salivary glands so you'll be extremely thirsty AND tasting balance is off so bitterness is enhances and wine is not at all enjoyable).
There was a lot of motion on our way down to the Bahamas from PC, so I put the patch on right before our first dinner, around 8p, which was about 3 hrs after we set sail. I took it off two days into the trip because it was making me run back up to deck 11 multiple times a day for water. I could not get enough water! The effects lasted another 3 days once the patch was off; I could tell when my taste buds and thirst level returned to normal that the meds had run their course.
I chose a midship, mid-low deck cabin (6596). I never felt sick in my stateroom, though I could really feel the ship swaying and surging forward as I slept and we sailed that first evening. And I again felt swaying and surging on last evening as we hightailed it back to PC from CC, but I slept much better, since I was used to it. I would not have gone higher than Deck 8 nor lower than Deck 5, though. I ran around a lot with my son (playing Midship Detective) and I have to say that I actually felt the MORE swaying movement in the lowest decks, like when we were in the dining rooms (decks 2 and 3). One factor might be because on those decks, we didn't have windows out to the sea. And we could sometimes feel the engine vibrations. I could also feel the ship moving when we were in the Walt Disney Theater; we always sat in the balcony and it would sometimes feel like the entire loge was moving. Aside from those times, we completely forgot we were at sea and not in a real theater.
I usually felt better on an outdoor deck where I could see that we were moving, allowing my eyes and body to reconcile their two sensory inputs. Having a verandah was helpful for that very reason. So deck 11 and deck 4 outdoor areas were great go to spots.
And the trick I learned on the Galapagos cruise is that if you're feeling ill, get into a body of water -- a hot tub, a pool, a bathtub full of water -- then your body and eyes will be able to better reconcile their sensory inputs and you will feel better. (I was a neuro major so sorry for the slightly scientific slant to the advice.) You can get your wife into the Rainforest Room hot tubs and have her just chill out there for a few hours. Or even in the adult only pool. It really helps attenuate the seasickness.
On a side note, my son got very seasick on our catamaran out in Hawaii in December, where he took a kids Dramamine that knocked him out for a nap, and then he felt better, especially once we picked up speed after the snorkeling (where he did vomit and lots of fish flocked to eat it up). By comparison, he said he felt no movement while on this cruise, and he even slept in the bunk bed that comes down from the ceiling! I had Ginger essential oil on cotton pads for us, since Ginger helps with motion sickness. My son hated the scent and said it made him feel sick and not from the motion of the ship! hahaha So that's not a solution for everyone, but a good one to know. Ginger capsules is a less smelly way to get that effect though not everyone's tummies can take ginger pills (it is a spicy spice, after all).
So depending on your itinerary, time of travel, and sea conditions, your family may need something as strong as a scopolamine patch (by prescription from your doctor, not to be used on children) or something just mild like acupressure/ginger/bonine/dramamine. Additionally, there is a zapper watch on
Amazon that does about the same thing as the SeaBands except with electrical zaps. For me, the electric shocking would be less uncomfortable than the pressure of those nobs on the SeaBand. I'm used to using a TENS unit at my old chiropractor so I actually enjoy getting zapped. LOL
When it is smooth sailing with good weather/calm waters, I discovered that I probably didn't really need "help" except on first night and I could have taken off that patch after just 24 hrs; I suspect SeaBands may have worked just fine but didn't bring to find out.
Have a great cruise and I hope it turns out that your family can sail just fine without motion sickness aids!
I assign you the task of getting some Bonine ahead of time. Take it for a day or so, and then go have a few drinks, in the name of SCIENCE, to make sure it doesn't cause an issue for you personally. It's just a sacrifice you have to make, for safety. LOL.
It was under $50 for the acupuncture "seeds" done in the DCL spa by their acupuncturist. My DD swears they were a huge help to her. She did take Bonine as well. She has such bad motion sickness that we use every tool available to us that seems to help. 
DD did say that she would be going to the spa upon boarding to get the seeds placed from now on, if she has not gotten an acupuncturist on land to do it right before sailing.
