Not sure there is to be honest mate. Lovely beaches and nice walks along coast, but not a load of entertainment for young uns. However it's only like 15 mins drive to Scarborough or Filey.
As suggested Fraizerthorpe is excellent for dogs (around 3 to 4 miles of beach) plus some old 2nd world war gun emplacements to explore...bit knackered now but something for kids to climb etc
You could look at Whitley Bay (near Newcastle) it’s lovely for a weekend and an easy 2-hr drive from Barnsley. Less commercialised than Brid etc Lots of dog friendly beaches.