Final answer:
Option 3) "Remember, if you wake Dickie, you've got to tell him stories..." best shows that Ted understands his mother's authority.
Step-by-step explanation:
The detail that best shows that Ted understands his mother's authority is option 3) "Remember, if you wake Dickie, you've got to tell him stories..." This detail demonstrates Ted's knowledge of his mother's rule and the consequences of breaking it. By reminding someone else of the rule, Ted shows that he not only understands his mother's authority, but also takes on the responsibility of ensuring it is followed.