All children know they have a father and a mother. Not living with one of the parents leads to psychological issues such as the feeling of abandonment. There plenty of studies showing that children with a parent who has passed away have less psychological burden than children living with one parent - losing a parent to death has been common in our history, so, it's something that we're adapted to. Divorce or not having a parent is a relatively new phenomenon.

I've heard that back in Soviet Russia, single moms lied to their children that their father has died in the WWII.