The National Trust's Croome Park is a good place to take the family.
The café serve good food (try their soup), yummy cake and decent tea/ coffee. Small gift shop on site. Plants for sale. Ladies loo has baby changing.
The house itself can be reached on foot or if you need a ride take a buggy ride down. I usually send the family off on foot and take the buggy.
The house itself is developing all the time and the restoration is going on all the time.
They have a small playground area near the main entrance and plenty of picnic tables near that in a quiet area.