This is a nice place to stay and relax and spend some rich family time, but it would offer much more in summer than winter. I stayed two weeks in December and had a lovely silent time (feeding cats :), but I missed the lively Acqua park and beach walks (all beaches are private and chargeable) as they were all closed - understandably.
The house has - literally - everything you need, and you would only fill up the fridge for the duration of your stay, buying from the nearby supermarkets (15 min walk away, or 5 min via electric taxis on return).
However, It is not a good idea to travel to metropolitan Istanbul frequently for shopping or tourist attractions; it can be costly and, most importantly, time-consuming (it takes 40-60 min on average on a ferry (they are frequent, though) and another 40-60 min in the metro or bus; one way). There are also some steep roads that you cannot avoid while walking - so perhaps something to keep in mind for those who plan to walk or hike in the island.