Esther, a brief visit to sail with pirates, eat Mickey ice cream, and fly with Peter Pan is vastly superior to not visiting Walt Disney World at all!
Obviously you must visit the Magic Kingdom. This classic theme park offers flying elephants, an entire mountain range to conquer, a castle full of Disney royalty, and a fireworks event that includes a flying Tinker Bell.
Do your kids love Star Wars, Pixar, or the Muppets? If so consider Disney's Hollywood Studios for your second park. Young padawans love Jedi Training Academy and the chance to travel on Star Tours while Muppet groupies will enjoy the 3D show staring Kermit and the gang. Experience Toy Story Mania and meet Woody, Buzz, and your favorite monsters for your Pixar fix. If you are a family of thrill seekers Hollywood Studios will keep your family happy with the fast and fabulous upside down flipping Rock 'n' Rollercoaster as well as the excellently themed, multiple dropping attraction The Twilight Zone Tower of Terror.
Do your children adore animals? Then Disney's Animal Kingdom should be a top contender for your second park. Travel on Kilimanjaro Safaris for an adventure among African animals, look for the elusive yeti as you travel full throttle on Expedition Everest, or enter the Tree of Life to see insects in a new light in It's Tough to be a Bug. Journey by train to the Affection Section and check out extinct creatures in DinoLand U.S.A.
No matter which park you choose for your second day your family will be ecstatically happy so no worries. If you have more questions about planning your brief but magical visit please contact me. I would love to help!