You’d have no issues apart from the air quality question. And, it’s a big question. Talk to your doctor about it. Other than that, Shanghai would be fine for your kids. For the dog, there are ways around quarantine, assuming you have the money to grease the wheels. Pudong is a very big place but I am assuming you will be in someplace like Jinqiao ro Kangqiao where the schools are, in which case yes you will need to have a driver as it’s not really ‘the city’, it is very suburban and difficult to manage otherwise.