I have a 6 year old. It's hard. We came from the US. Quality of life here is very low compared to a US middle class neighborhood. Air, water, soils as were mentioned are poor. Compared to other Chinese cities HZ is relatively better. But compared to any US city its far worst. Think LA or SLC in winter at their worse, this is an average day here. Then there is public safety. Roads are treacherous, my child is scared to cross the road here because she has been nearly hit so many times. There are exceptions but in general people are inconsiderate, selfish and downright clueless. Its everyone for themselves all the time.
Your kids' Asthma will likely get worse. Accept that as a fact. Summer is very hot and very humid. Winter is fairly mild compared to northern US, comparable to mid-Atlantic. Few nights below freezing. But also very humid. Rainy season is hell.
People hangout indoors a lot. Malls are very popular. We do a lot of hiking in the winter. HZ has a great network of trails all over the hills and its nice in the winter. Visiting tea growing areas, an excellent botanical garden, lots of flowering trees throughout the cooler months into spring. We worry about air quality, but we still have to go out. We love hiking, its our thing and we would go insane without our weekly long walks. But yeah, it sucks. I cleaned out some computers in my office this week and was terrified by the gunk that had accumulated in the fans filters.
There are cheap flights to Japan, lately, we go alot. Skiing, hiking, fishing, visiting friends. Its close and an easy escape. The country side in western China can also be beautiful, but travel more restricted and logistically complicated. If you have a Chinese employer you will take vacation at the same time as everyone else making travel miserable and crowded so it makes it hard to enjoy anything good that China has to offer.
We dearly miss our life back stateside and we look forward to returning once the political climate improves. In the meantime we will be spending our summer outside of Hangzhou so my daughter can enjoy some healthy air ( Japan and Canada this summer).
In conclusion, if I had to do it again I would not bring my child here.