Some additional data (from the perspective though of a late-30s single guy rather than a family)...
There are many expats living in other cheaper areas - HK is not heavily "ghetto-ised" like a lot of cities with expat communities. I find this actually makes it a little harder to get into a social scene since being an expat doesn't automatically confer "membership" as it might in other places (in my experience including Taipei & Moscow). However, if your kids are schooled here then there is automatically a social scene attached to that I guess.
It seems that many expats move first into one of the areas Alpha Leader mentioned (also Discovery Bay, which in my view is a weird place that isn't really HK - it reminds me of "The Prisoner" - but it is very convenient for Chek Lap Kok), but often move out to other areas after a year or two when they have found their feet. Rentals in places like Sai Kung will be dramatically cheaper, and you might even be able to find a place with something that approximates to a small garden!
If you live on Hong Kong Island itself you will probably find running a car prohibitively expensive - the parking space in some apartment blocks can cost HK$4,000 per month to rent, and then you have to pay to park everywhere you go as well. However, the public transport system (underground & overground rail, various types of buses, and ferries) is the best I have seen anywhere in the world and very reasonably priced. Taxis are also plentiful and fairly cheap.
The other thing you will find is that almost all families here with kids take on an "amah" - a full-time, live-in maid. These work in a regulated way with employers paying a fixed wage of just under HK$4,000 per month plus room and board. Most are from the Philippines, with some from Thailand, Indonesia, etc. They will do all the shopping, cooking, cleaning etc for you, leaving your wife free to have her own career or brush up her golf!
Happy to discuss by email if you want more.