Head a bit further south into North Derbyshire. With the peak district and all it has to offer , climbing, potholing,major cities, etc. Lots of safe bike rides , country houses and castles although probably not too appealing for the 8 to 12 year olds. Matlock, Castleton, Eadale, Eyam, Chatsworth, loads of places. Lots of old , disused rail routes for easy cycling and walking.
There are outdoor adventure centers offering cragging, climbing , potholing.
Then again look towards staying in W Yorks and you have easy access to Skipton, Harrogate,Leeds, Derbyshire, York, not too far to Scarborough and Whitby, as prev poster mention theres Malham( fantastic place). You would be very close to the peak district.
Wharfedale, the Ribble , there is xscape in Castleford ( indoor winter sports),eureka in halifax, magna in sheffield.
Loads to do, but it all depends on what kids 8 to 12 would like. I have difficulty getting my 10yr old out of bed these days.