problem with tsing yi esf is that it is ONLY kindergarten. i think the primary school for that area is beacon hill (?). i'm not sure what the enrollment prospects are for that school, although i have a friend whose daughter goes there and seems to really enjoy it.
no reason you have to/should leave your dogs in sydney, especially considering that is not where you are originally from. there are MANY dog owners/lovers in hk, lots of places you can take your dog (although not many places you can take big dogs off-leash), and lots of options for boarding/kenneling when/if you go on holiday.
if hubby commutes by car to ifc, then even as far out as sai kung country park is less than an hour. for around $30k in the country park (prices have risen dramatically), you'd get 2100' house with 4-5 bedrooms, 4-5 bathrooms, car park and a small garden.
you could also look at hong lok yuen. i've not been there myself, but heard good things about it. again, i would suggest commute by car rather than public transport.
public transport in hk is fantastic, but honestly, with 3 kids i would strongly suggest a car, unless you live right in the thick of hk island (and you'd get a shoebox for your budget there). standing in the pouring rain waiting for a minibus/bus/tram or walking to the MTR station is NOT something i would want to be doing with 3 young kids! neither would i want to do it in the 33C + 98% humidity we often experience in the summer!