I am guessing that our spouse and child are not dead. This is solely based on the fact that you not only customize your own appearance but also that of your spouse, and resulting from the two individual faces your child will have a unique appearance. So why would you be able to go through all that trouble of customizing your spouse and subsequently your child if they die within the first hour or so of the game? My hypothesis is that they went into the vault with you and they left the vault before you for some reason, thus they are still alive in wastes or some impact of their existence is left out there for you to find.