💡 Detailed Explanation
The correct choice is Option 2: 'Director, I'm not feeling well, so would it be alright if I left early?' Since the speaker needs to ask their boss for permission to leave early, they must use the polite request pattern '〜てもよろしいでしょうか' (May I...?) with the verb '早退する' (to leave work early). Option 1 ('お先に失礼します' - Excuse me for leaving before you) is a declaration used when actually walking out AFTER permission is already granted. Option 3 ('休んだほうがいいですよ' - You should take a break/rest) is an advice directed at someone else, which is extremely rude when said to a boss.