Hi Yasmin:
For relaxed atmosphere and privacy only, I would have suggested the
Treehouse Villas at Saratoga Springs Resort. The villas are very large and comfortable, nestled in "trees" providing a relaxing environment. However, if relying on Disney transportation, the Treehouse Villas are not your best option as you must wait for a bus to get to the main Saratoga Springs building and then transfer buses to take you to the Parks. I would not want to spend extra waiting time on vacation waiting for a bus transfer. Between
Fort Wilderness and the Tree Houses, there are more family activities at Fort Wilderness, but the Tree Houses are more private and have better ambiance, in my opinion. However, you'll have the same bus transfer transportation issue at Fort Wilderness.
To meet your three criteria, I believe your best bet will be a two-bedroom villa at
Saratoga Springs Resort. For me, a big advantage of Saratoga Springs is that parts of the Resort are within walking distance to the restaurants, shops, and attractions in Downtown Disney. In addition to quick and easy access to Downtown Disney, being close to Downtown Disney also means you can also take advantage of direct buses from Downtown Disney to other resorts. Request a room in the Congress Park section of Saratoga Springs to be close to Downtown Disney.
Again, if you had a car, I'd probably recommend the Treehouses to meet your needs of atmosphere and privacy. However, without a car, Saratoga Springs is likely your better bet. If you think you won't be bothered by the bus transfer, then consider the Treehouses.
Enjoy your vacation.