If you're able to connect to someone else's wireless, your computer is not likely to be the issue. Unfortunately, we can not access your host family's wireless, so we can't check the settings. However, there are various security settings that can be stored in a router to prevent others from connecting. Most likely, your host family has some security settings on their wireless. Their neighbor has unsecured wireless, which is why you are able to connect.
Software Support Specialist, Computing and Network Services