Hi
I think my first point would be my most blunt: if you or any of your children are currently having diagnosed respiratory problems, than I would seriously reconsider a relocation to Hong Kong. If you have a problem already, coming into a more polluted environment could make things a bit worse.
However, while many people are very concerned about the air quality, when you live here you can still find a way to do things in this environment. We do not let our children to play on bad air quality days, opting instead for them to play indoors in our building's playroom which has some filters running. We avoid, when possible, their travel to highly polluted areas (such as Central) if the pollution is above a certain level. I've cancelled their football practice in Happy Valley on particularly bad days. Our school also limits outdoor recess if the API is above a certain amount. We also run HEPA filters in our house, one each in the bedrooms with the kids and a larger model for the living room, all in an attempt to keep things a bit more manageable.
Basically, we check the pollution levels more often than we check the weather, and treat bad pollution days like bad weather days.
Some people rationalize away the pollution by attempting some comparisons. "Well it's not as bad as Beijing" or "the South Side seems better than Central" but the reality is that air pollution should be compared to one standard: what is healthy, and what is not.
At the moment, and for most of the last few weeks this Winter, the entire island has been covered in what is considered "unhealthy" air by most Western government air quality standards. As of this morning, the air is a 'Code Orange' air quality day by US standards (with one station reporting 'Code Red'). Every station in Hong Kong is current > 100% of the World Health Organization maximums, and Causeway Bay is currently over 200% of the maximums (by the end of the day it will likely reach 300% of the maximums). We are a level 5 out of 6 on Australia's air quality index (Very Poor Air Quality) and about a level 7 out of 10 by UK air quality standards.
This is the app I wrote which will help you monitor the air quality by western standards. It's free for the iPhone.
https://itunes.apple.com/us/app/hong-kong-air-pollution/id504536152?mt=8
You can "try" to live in an area with less pollution, but it's really kind of like the situation of "what part of Hong Kong will stay dry when a typhoon comes to the city?" The South Side of Hong Kong island "seems" better by many--the air doesn't "look" as bad as it does in Central, but the government has refused all requests to put in a air quality monitoring station so there is no scientific proof that I've seen that proves it is better than other parts of the island. Still, many try to live in areas further away from the Central business area (cars), the power plants (coal exhaust) and the cargo ports (ship exhaust) in an attempt to get further away from some of the main local source of pollution. Unfortunately when the Winter winds shift and bring the air down from the factories in China, there isn't anyplace you can really hide.
There are good days, even good stretches. For example we had a nice run this Fall of several weeks, months even where the air was below the maximums in most parts of the city (the Central Business district and Causeway Bay will top the maximums pretty much every day due to the lack of air circulation and abundance of vehicles). But other parts of the city will report generally good air quality such that you aren't as concerned running around and whatnot.
It's all a bit of a trade off. As I mentioned at the start, if air pollution is a significant medical issue in your family, than whether to live in a certain part of the city with air filters isn't really the question--whether to live in Hong Kong is what you should be asking. If you are still interested in the city, there are ways to mitigate some of the dangers but you will want to pay close attention to your children's health and lung development as they grow.
Good luck with your move.