It is funny to read that, very typically under appreciated by the locals.
As I originally said Littlehampton is a tale of 2 towns.
The waterfront & everywhere else.
You've got a full day and more from The Look & Sea centre, just up the river, round to Mewsbrooks Park and the swimming pool.
But...
For a 6 and 3 year old I'd skip Worthing.
Just head for Littlehampton, and make sure you can see water.
DO NOT LOOSE SIGHT OF THE SEA OR RIVER.
Prom along the seafront, and river.
There's plenty to do, mini train, life boat station, golf, amusements inc plenty of penny push, posho restaurant...