I think it's quite possible your family didn't make it into the vault with you or that they themselves escaped prior to you, perhaps your vault did receive a GECK and some of the experimentation went wrong, or your family were turned into supermutants?
I find it hard to believe that the PC's personal life will have nothing to do with the main story. There has to be something pushing the story forward, like how the PC was trying to find his/her dad in FO3 and track down his/her attmepted murderer in FNV.