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 is a great place to visit.

Calypso Bay Water Park was recommended as a nice place for younger kids.

A water park for older kids ages 13 and up that was recommended is Rapids Water Park.

WannaDo City - about an hour drive but so 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 is CityPlace.

Find a state park to hang out at Florida State Parks.

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 looks great.

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

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

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.