Which crisis shows the children a surprising skill their father possesses? What has Atticus kept this a secret?

I think that you are referring to when Atticus shoots Tim Johnson, the rabid dog. This takes place in Ch. 10 on pg 96 (in my copy). Atticus turns out to be an expert shot with a rifle. Jem and Scout are so surprised. Mr. Tate tells them that they used to call Atticus "one-shot Finch." Harper Lee wanted an avenue to show Atticus's kids that Atticus can do something traditionally "masculine" like shoot a gun and hit a target. Atticus is of course very humble about it but Scout and Jem are impressed.