We visited this Easter and had a great stay. This is  a site with a very rural look and feel, situated at the end of a single track lane. However the local traffic was incredibly busy, with significant queues around the site entrance at Baslow. Also for a family, the entrance fee to Chatsworth is a bit on the steep side, particularly for those with a National Trust membership. The Park is also incredibly busy with cars seemingly parked everywhere- which does detract from the rural beauty of the place. I would try and avoid Bank Holidays or even school holidays if possible.