Croc Cottage, Flookburgh, perhaps?
http://www.soul-trade.com/croc/croc.html
Dogs are welcome, there are 2 pubs nearby (The Crown and the Hope & Anchor) and a village shop. It looks to be a good base for touring South Lakeland.
or Apartment 1 (which accepts dogs and sleeps up to 6) at Langdale View, Bowness-on-Windermere:
http://langdale-view.co.uk/
There are plenty of shop and pubs, and you're right at the heart of the Lake District.