Cruises are a great way for families to travel and see a variety of countries and ports. Ships are very safe and kids over 6 can roam freely on their own for short trips. Some ships also offer babysitting services and daycare centers. It is unlikely that you will notice any motion on a large cruise ship, even if you are sensitive to motion in automobiles or airplanes. All ships today have stablelizers to smooth the ride.
Some cruises sail calmer waters than others.
Caribbean and Alaska cruises enjoy smoother sailings than say Bermuda. If seas do get rough, there are many preventative medications available on board. There are dozens of activities going on all over the ship every day. Relaxation is what attracts many people to cruise travel. Every ship has one or more pools that you can lay around with a good book, most have a library and several lounges where you can sit and relax by yourself or with friends.