Hi,
I know of a place accommodating many dog-owners. It is a new property development consisting of about 30 blocks of apartments called Park Island in Ma Wan. The developer has been successful in turning a small fishing vallage into a mordern building project. The theme is on resort-style living in a suburban environment. Please view developer's website for more information:
www.parkisland.com
You may visit the place to feel it personally. There are several ways to reach there, viz. by ferry from Central (Pier No.2) close to IFC or by MTR to Tsing Yi or Kwai Fong for transfer by shuttle bus.
There are many units available for rent, in different sizes, facing and layout (some with balcony). There are lots of open space and greenery in common areas there are suitable for dog-lovers and kids. You may approach some of the real estate agents there to find out more.
A note of caution: In Hong Kong, if 2 of your neighbors lodge a formal complaint against your pet, your building management can forbid you from keeping it. But I don't think this may happy in Park Island on account of the vast number of dog-lovers there.
Good luck.