the saying is usually "a bad apple doesnt fall far from the tree" meaning that if the parent is bad (the tree) then the children (the apples) even when they fall off and leave the tree are still likely to bad.
its not, its on bad apple spoils the bunch and the apple doesnt fall far from the tree. If you google a bad apple doesnt fall far from the tree you will just get lots of references to an apple never falls far from the tree.
This was also used in Batman Begins recently when a dinner guest says 'The apple has fallen very far from the tree, Mr. Wayne' i.e. he is a poor reflection on his well-respected parents.
As I mentioned to someone just a week ago or so on this site, check out the song with the same title from Kander and Ebb's musical The Rink. Sung by an estranged mother and daughter who discover they have more in common than they thought.