You do pose a rather difficult question, because treating children with pharmaceuticals is always a challenge. Adn unfortunately, you probably won't enjoy hearing what I will have to recommend.
Of the treatments generally discussed which usually don't cause drowsiness, only the homeopathic remedy using ginger may be used. (I don't know if SeaBands are made in a pediatric size for your toddlers.) I would recommend using the ginger candy, if they will take it. The clinical studies on children have not been performed formeclizine products (Bonine, etc.), and are not recommended for children under 12 years old. Additionally, the meclizine products aren't made in a dosage form which can be conveniently given to children, to my knowledge. Scopolamine patches are not prescribed for children.
This leaves you with the dimenhydrinate products (Dramamine, etc.). Dramamine does come in a chewable and liquid dosage forms (I know this, because my company makes Dramamine, and I used to support its manufacture) intended for dosing children. Depending on the size of your children, I would recommend dosing them with 12.5 - 25 mg (1/4 - 1/2 tablet, or 1 teaspoonful [5 ml]) every 4-6 hours, to a maximum of four doses per day. And, yes, dimenhydrinate products may cause drowsiness, but in children, just the opposite effect (restlessness or insomnia), known as paradoxical effect, can occur in children.
The other thing to try is to keep the children out on the open decks, letting them see the horizon and gulp fresh air.
I know these probably aren't the answers that you were hoping for, but to my knowledge, these may be your only alternatives that I can recommend.
I hope you and your children have a smooth, trouble-free, and thoroughly enjoyable cruise, Linale!
John Burns, R.Ph.