You did not say when you will be going, I will be there in June.
They do have great beaches on the west side of the park, a kayak rental for the brackish water area where you can see manatees and dolphins. I am not sure what activities your children like to do but when I was a kid the beach had all my interest.
As someone mentioned earlier there are other sights to see in St. Pete and Clearwater including an aquarium in Clearwater. The St. Pete Pier is popular, there are boat excursion to the key/island off shore, all within a reasonable drive.
There are many families that stay in that campground in the park with children, you will be in good company.