Ben if the wife n kids like walking then there are plenty of routes in the woods , I found out about the place whilst walking the dogs and used to park at the far car park (furthest away from bike routes ) and the missis would take the dogs for a walk for 2>3 hours whilst I did the bike routes , alternatively it's not to far from Settle and Ingleton if thats more in there line of things to do (White Scar Caves are about 20 mins away but it's pricey to get in AFAIK). My caving was always done more off the beaten track .
I'm guessing to get to the new car park you just drive past Cocklett hill (north) until you see the sign to turn right to the new hub car park ?.
Matthew