They don't have to reach the sink, MrsWembley. They can run it under a tap. There's always a tap somewhere on a campsite surrounded by knee deep mud where other kids have run their plates under the tap
I have another tip for you. In fact I have lots of tips, but here's one:
If you are camping by the seaside get them wetsuits, onsies, and wellies a size too big. That way you bring them back from the beach in their wetsuits, take them into the campsite shower, strip off wetsuits wash them and the suits, change them into their onesies and wellies, and march them back to the tent/caravan. If you don't like onesies, try towelling dressing gowns. But then you need thick warm socks.