Who is the object and subject in this passive sentence?

Question

I came along a conversation between two characters that have a sort of rivals-to-lovers relationship. There's only two lines of dialogue, but I can't place the meaning.

Person 1: 僕に愛される気あんの?

Person 2: ほら, その気にさせて下さいよ

Which I took to mean

Person 1: Do you feel loved by me?

Person 2: Look, let me care for those feelings

I believe that what's supposed to be conveyed here is that person 1 is questioning either his love for person 2 or her love for him. Then person 2 is somewhat confirming it.

But honestly I'm so lost as to who's feelings are being referenced with "気あんの". I also don't understand who is loving who using the passive form with 愛. In addition, my translation sounds horribly stilted, is there a better way to express this?

Answer 1

「気」here means "feel"/"feeling" in the sense of "to feel like doing something".

行く気がない → to not feel like going
やる気がある → to feel like doing (something)

So

僕に愛される → to be loved by me
僕に愛される気 → feel like being loved by me
僕に愛される気あんの？ → "Do you (even) feel like being loved by me?" which sounds more natural as "Do you (even) want to be loved by me?"

In a similar vein, 気にさせる can be used as the causative of 気がある to mean "make (someone) feel like doing (something)"

So

その気にさせる → to make someone feel like doing "that" (being loved by person 1)
その気にさせてくださいよ → "Make me feel like doing that (being loved by person 1)" or more natural-soundingly "Make me feel like being / want to be loved by you"