The kids can go to the shows no problem. They have a great magic show that the kids will really enjoy. Most of the shows are around 8:30. we found that if we ate between 6 and 6:30, we were able to make it all shows on time. If you think you are pressed for time, tell the waiter you're going to the show, and he'll kick it up a notch.
They have movies in your room and in the theater (Dawn) that are not yet out on video but have been out at the theaters for awhile. Don't know about the majesty having a theater but my guess would be that they don't. On the Sea they had a small screen that they would set up in one of the lounges, but only on days that we were in port.
Forgot to add....on the Dawn in November they showed Pirates of the Caribbean. That was a week or so before it came out on video and they showed it in the Stardust Theater first and then the regular theater and in the staterooms later in the week. The first showing was an "in port" day but it was later in the evening and they were expecting a larger than normal crowd for it. The screen in the Stardust was huge, just like being in a regular theater.
Just got back from the Dawn yesterday. There was a sheet in our room the first day listing the movies for the week, and the daily freestyle had the times for you the night before. We had Cheaper by the Dozen the first night, and the LOTR#3 the last day. Most of the ones in between were more adult movies. Movies also run all day long on your cabin TV. Children can go to all the evening shows in the Stardust, but may or may not be interested in them. My 10 and 12 YO brought books with a book light and used them during Bollywood and Miami Rave. The comedic juggler was the best for kids.
We were a group of eight, so we had dinner early most evenings to avoid a long wait. If you eat by 6:00, you usually won't have trouble making the 7:45 show. The only show that really seemed to fill up was the variety show the last night, which only had one showing. The gymnast and the juggler were very amusing.