I have done a route plan from Stirling to Hull and assume you are coming down the A1 and A1M and then turning West down the M62 to Hull.
Based on this route Leeds / Wetherby, which is WEST of the A1M, would take you out your way.
Whereas EAST of the A1M is York which is one of the most amazing cities in Britian. Also by going to York you could cut the corner off and go direct from York to Hull (have a look on the map and see what I mean).
It is about 45 miles from York to Hull.
York has the National Railway Museum which would amuse anyone for a few hours.
http://www.nrm.org.uk/home/home.asp
Also in the centre of York is York Minster, one of the greatest building in the UK
http://www.ada-auth.org/arg-photos/28/Minster- 1-Thumb.JPG
There are also loads of city walls round the city and the kids would have great fun running round these, that should work off some energy.
http://www.callipygia600.com/allpictures/scotl and/images/yorkshire/10_york_walls.jpg
The centre of York has some amazing medieval buildings, narrow lanes and fascinating shops
http://www.mikejs.com/pics/2001/york/shambles1 .jpg.
I think York would be a great stopping off point. Problem is keeping it down to 2 hours !