The Green Caravan Park Wentnor,has a stream,rather than a river but is nice for kids to have a paddle(..don't be put off by the "caravan park" bit,in the title.)
Off Topic this bit ...Can't say I've ever noticed a stream there but for a really quiet,"remote feeling",basic, woodland site,that's not far from you..take a look at Rocks East:
Nantcol Waterfalls is a fab site, in North Wales though. We don't have young children but there were quite a few at the site all enjoying themselves in the river, on the rope swing. Lovely site in a fantastic location.
Don't forget to leave a review of the campsites you have visited this year or last!