My parents have a vacation condo in Lake Worth, FL which is near the West Palm Beach area, but it is not close to Orlando.  When we were going down there last summer I had to do some serious research since that area is more for retirees.  But you would be surprised that I found plenty of stuff for us to do with our kids who at the time were age 4 yrs and 1 1/2 yrs old.  

 I found a lot of stuff to do but here is what we recommend as MUST DO:

Lion Country Safari  www.lioncountrysafari.com

Calypso Bay Water Park was recommended as a nice place for younger kids  http://www.pbcgov.com/parks/aquatics/waterparks/calypsobay/ 

A water park for older kids ages 13 and up that was recommended is Rapids Water park - www.rapidswaterpark.com

WannaDo City http://www.wannadocity.com/  - about an hour drive but SOOO WORTH IT!  I suggest you call ahead to get their hours b/c they do not always update their website and the summer hours change.  Our kids LOVED IT!

Nice place to walk around and shop in West Palm Beach http://www.cityplace.com/

Finding a state park to hang out at  http://www.floridastateparks.org/capeflorida/ 

We did go to the beach but I forget which one it was. 

 Things we wanted to do but never got around to it:

Southern Florida Science Museum-  www.sfsm.org

The School house Children's Museum (They also have a great park right behind the museum). 

http://www.schoolhousemuseum.org/index.php?sid=1b33c914388c592ce0adb891d6ae028f  

The Palm Beach Zoo is also a good choice (pack a bathing suit because they have a fountain the kids can run through)  http://www.palmbeachzoo.org/

Beaches that were suggested but didn't get around to going: Juno Beach has bathrooms across the street at the parking lot. There is a beach in Jupiter called Dubious that is great for small kids.