Hi,
a couple of years ago my family went on a similar holiday, which was a great success.
We stayed in a villa in a private estate called 'Quinta da Lago' near Faro. It was amazing - beautiful, luxurious villa, all large bedrooms ensuite, huge pool and gardens, option of cook/maid/gardner, about 2km from beach, many restaurants nearby, villages nearby.
Price approx 3000stg for a week including hire of 2 cars (not too bad when devided out among the adults)
I cant remember who we booked with, but will check and post back. Or you could google 'Quinta da Lago'.
Cheers.