Father is adamant that mother and the children stay at Out-With. What are his reasons for this?

It's hard to understand Father's reasons for taking his family to the camp when their lives would have remained somewhat constant had they stayed in Berlin. We can only infer that he didn't want to be separated from them. Possibly, the Party wouldn't have approved had he left his wife and children behind. Maybe.... he was worried about their safety and wished to keep them close.