I only bring that up to point out a cultural difference that other cultures might see this differently
https://answers.yahoo.com/question/index?qid=20101116164518A...
However, it is common in Sweden to respect unwritten laws and social conventions. Many neighbourhoods also have neighbourhood watch and such things. I haven't lived there for over ten years but I'd imagine not taking shortcuts through neighbourhoods with children would be a convention most swedes will respect.
There is a traditional free right to roam, but it does not extend to gardens and areas next to houses. Outside of that, it is rather permissive.
Back on topic but still in Sweden: more or less all shortcuts in residential areas are closed, either by physical barriers, or more commonly by official signs forbidding pass-through traffic, and they are typically respected.