The places I've heard of that are best for kids are;
The Gold Coast, Parkview, Bel Air, The Belchers, No 80 Robinson Rd -none of which are close to where you want to be so that is not very helpful.
It seems that you get the best results on this website if you publish a really specific request ie: Apartment near x school and then people close to there will reply - I know there have been some long threads in the past about that area so try doing some searches for them. The Laguna Verde place mentioned above looks amazing and might be worth checking out.
Don't envy you doing the hunt with 3 kids but seems like there is no other way. Highly recommend you bring snacks with you for the first few days of looking. I know that until I found my way around I got really frustrated finding somewhere I wanted to eat between looking at places and I bet your kids are even fussier than me.