I assume your husband works in downtown Toronto? I used to live in Oakville and had a couple summer jobs in downtown Toronto.
In any case, the main highway that runs from Burlington/Oakville to Toronto, the QEW, tends to be quite congested, especially around Trafalgary Road in Oakville (Trafalgar Road is also congested in the mornings and afternoons). The QEW changes names in Toronto, where it can also be congested. Fortunately, this area has the best commuter rail line (GO train - Lakeshore West) in the Toronto area, and most people this area commute to downtown Toronto by GO train. The express trains are before/outside his start time, so the train ride would be 30-60 minutes depending on where exactly you would live. Then it's just a question of how far his workplace is from Union Station and how far you would live from the suburban station. Pickering is a suburb too, I think it's a bit more affordable than Burlington/Oakville, but is ethnically it's similar, and for commuting, it's similar too, with the GO train being the best option (45min ride) since driving would involve taking the DVP, nick-named the Don Valley Parking-lot.
Is your daughter quite competitive in gymnastics? My sister joined that club as more of a beginner/intermediate gymnast, but the place was crowded and she spent most of the time waiting in line to use the equipment and wound up joining a club in Mississauga that turned out better for her. But maybe if your daughter is already quite talented she'll be able to get more time on the equipment?
The one thing about some of the neighbourhoods you mentioned is that they are relatively expensive. While they usually have housing at a more affordable price, those would be mostly in smaller houses or apartments, so what sort of home and budget are you looking at?
As for Oakville/Burlington being predominantly white, that's mostly true... I would say about 60-95% depending on the specific neighbourhood, but mine, which was probably around 85% white didn't seem to have any problems. The Asian kids seemed to be fitting in fine, so I wouldn't worry about your kids fitting in, especially if they're comfortable in English and are familiar with North American pop-culture. In neighbourhoods with higher proportions of Asians, there could be more of a tendency for kids to stick to their own race.
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