Upvote:3
Your family's history does not appear relevant. The application form does not ask for the name of your parents or other relatives. It might be possible to guess that your mother is your mother based on your respective names but depending on the locale/culture, there might be no way to tell or many people with the same name. If consulates were taking decisions on that basis, they would therefore take the trouble of asking more details to be able to run a proper search.
It might be different if you are all applying at the same time or within a short time frame.