Final answer:
The second theme of the first movement in Mozart's 'Eine kleine Nachtmusik' is in the key of D Major, which is the dominant key of G Major, the overall key of the movement.
Step-by-step explanation:
The key of theme 2 of movement 1 in Wolfgang Amadeus Mozart's Eine kleine Nachtmusik is D Major.
The first movement, which is in sonata-allegro form, typically features a transition to the dominant key in the second theme when the piece is in a major key. In this case, since the piece is in G Major, the dominant key is D Major.