My Sister in law took Dramamine for a cruise a few years back...the regular adult recommended dose. She slept for 30 hours and missed a day of the cruise. She has since cruised many times, never takes motion sickness medicine, and has never had sea sickness. The effect of the medicine was by far worse than anything she has experienced on sea.
I, personally, would be very cautious to give my children a drug for a problem they MAY have without knowing the possible effects of that medication.
Now if I was sailing through a hurricane, that would be different, but in good conditions the movement of the ship is not that bad. I want to add that I am not a good car passenger, getting motion sick very easily, nor can I ride on most amusement park rides without losing my lunch.