Welcome aboard, Edna! Disney Cruise Line has themed dining nights most nights of your sailing. You didn't mention which cruise you'll be on, but I can tell you about a few of the evenings that you can expect.
Cruises of six nights or longer will have a Formal Night as well as a Semi-Formal night. On these nights, I've seen anything from ball gowns and tuxes to simple summer dresses and men and boys with collared shirts and a tie. It's really up to the guest, but I always say why not go fancy? How often do you get the opportunity back home, and it sure makes for some great photo opportunities.
The shorter cruises will include either a Semi-Formal only or an optional dress-up night on the 3-night cruises.
Each cruise will have
Pirate Night, where pirate gear is not exactly required, but highly encouraged! There are plenty of options in the ship's shops, or you can bring your own pirate gear from home. All guests will receive a Pirates IN the Caribbean bandana to wear.
Then, of course, you'll find a few cruise casual nights. Disney does suggest no jeans (though anything goes if you're in pirate gear that night!), and asks that long pants are worn in the main dining restaurants. I've seen many little boys, mine included, who wear a nice set of shorts and polo shirt, so that's fine for the little ones.
I hope this gives you some idea of what to expect. Let me know if you want specifics for your cruise sailing, as I'm happy to help you with more details! Have fun planning, Edna!