Your initial list of housing requirements is a big ask ... to find a full village house (3 floors, 200m. sq. + rooftop) within an hour's "uncomplicated" commute from Central at 40K per month - might be possible, but don't count on it. South Lantau would tick all the boxes except the uncomplicated commute. I reckon your best bet would be to look at village areas out in the New Territories which are served by express bus routes into Central - although you will probably need to walk a bit to reach the bus stop (we do NOT have commuter car parks here).
I don't know if you've investigated what "villages" are like here - many (most)? are cheek by jowl, often semi-detached, 3-storey concrete boxes, with every scrap of ground concreted over. Maybe you already knew that, but I don't want you having any romantic notions before you arrive. You also need to be aware of dogs (semi-feral in some villages), and the noise of mahjong games, karaoke and Chinese opera ... it can be a lot noisier than living in a unit.
Be aware that there are some nice medium-density residential developments with ecellent facilities and running-around space for children. Some, like Ma Wan and Gold Coast have easy access to still-water beaches and natural parkland, so if you do give up on the village idea you don't have to be surrounded by concrete and 40 floors up.
Childcare here is usually means-tested, for working class families, and all in Chinese. For everyone else, a live-in helper is the way to go if both parents are working.
Give yourselves a 6 month trial without a car. With the public transport here, they honestly can be a lot more trouble than help.