If you truly care for your cousin (as you claim to), you’d accept her as she is rather than ostracize her for what you perceive to be a negative attribute. She is the only one who can judge her comfort zone and energy level (as you don’t walk in her shoes and haven’t lived her life), and she is, moreover, entitled to her preference.
Your cousin, I suspect, does not take issue with your lifestyle, recognizing that no two people are alike. She furthermore sounds like the type who is comfortable in her own skin and is not afraid of being alone with her thoughts — contrary to some party animals who keep running away from theirs.
I’d give Serena some breathing room and respect our differences. And, incidentally, your pseudonym for your cousin is most apropos — considering that the word “serene” is defined as calm, peaceful and untroubled. But you knew that already, didn’t you…