The correct option is D cool as a cucumber.
A simile is a figure of speech that presents a likeness, or draws a comparison between two unlikely thing; it contains the words 'like' or 'as'. For example, as smooth as butter, light like a feather, and so on. In the given sentence, a comparison is made between the mother and a cucumber (because it's known for its cooling effect) as she remained cool. The phrase "cool as a cucumber" is hence, a simile (also, it contains 'like'), hence D is the correct option. "His mother" is the subject of the first sentence and does not compare anything. "Summoned by the cops" is a verb phrase containing the verb 'summoned' and the noun 'cops', and "pick up" is a phrasal verb. As these phrases do not perform the function of a simile, options A, B and C are incorrect.