We had a lovely stay at East House Farm in August, in spite of torrential rain for much of the week. It's a very comfortable place with everything thought of, a great fire, a wonderful collection of books and games, lots of space. The surroundings are amazing as it's in the most beautiful valley, with a rushing river nearby.
Great for walking straight from the door - high level or low. Real peace.
"Local amenities" seems an inappropriate question for this property as it's a long way from any shops and that's its magic. Hawes (7 miles away) is the perfect place to stock up and has lots of local shops, a market, museum etc.
We stayed here with 2 children and 2 grandparents and everyone loved it. (Note that it's in a collection of houses - they are close but it still felt private)