That's a tough ask!
If you're willing to go a bit further up, there's a couple at South West Rocks which is 6 hours from Sydney.
There's the Horseshoe Bay Caravan Park (right on the beach, but no fires). I've included a photo of the view from one of the sites from when we were there in April:http://han.chung.name/photos/HorseshoeBay.jpg
And there's one near Trial Bay Gaol (right on the beach, camp fires allowed) of which the name escapes me. Here's a photo of the beach that it's on:http://han.chung.name/photos/TrialBayGaol.jpg
If you want to go south and don't mind venturing into a National Park, I'd highly recommend Green Patch in Jervis Bay - right on the beach and they allow wood fires.
You mentioned kids, so all the beaches I've mentioned are sheltered swimming beaches.