In "Do Not Go Gentle" (Season 3 Episode 20) why did Elena leave the party and go with Esther?
In fact she was supposed to have a conversation with Damon and Stefan (far from the party but not outside the party room). The thing is Jeremy saw Elena walking away with the 2 vampires, and followed her because he worried about her getting into some dangerous plans, and also because he doesn't want her to hang out with the 2 vampires.
During the conversation, Damon proposed to kill Alaric, which is for him the only solution. Jeremy heard him and couldn't bear this idea of losing Alaric (who is like a father to him).
Feeling upset, Jeremy went away from Elena, and the 2 vampires. Elena saw how upset he felt and wanted to comfort him.
So, she tried to stop him walking away, and that's how Jeremy lead her sister outside the party...
There, after some sister / brother conversations, they met Esther who "forced" Elena to come with her (otherwise, she'd do harm to the ones she loves...)
Elena decided to follow her Esther to avoid hurting anyone.
Damon: We three need to talk. (speaking to Elena and Stefan)
(Jeremy sees Elena and the 2 vamps leaving the party)
Jeremy: Sorry. Uh (bumping into his ex-girlfriend Bonnie and his new boyfriend Jamie)
Bonnie: Why are you still wearing your ring? Didn't Elena tell you?
Jeremy: Yeah, yeah, I know all about Alaric. My sister stops hanging out with vampires, I'll take it off.
(Jeremy goes away)
Jamie: Uh, ex-boyfriend?
Jamie: That's not awkward at all.
(Away from the party)
Elena: If Alaric's sick, then we need to find a cure, something.
Damon: We tried medicine. We tried magic.
Stefan: Why don't we get him off vervain, compel him?
Damon: To do what, pretend to be Alaric? The guy that we know is gone.
We're talking about someone who not only hates vampires, but vampire sympathizers, which makes one of his most obvious targets I don't know you, you?
Stefan: What? You think he'd go after Elena?
Elena: So wait. What are you suggesting we do?
Damon: I'm suggesting that we put him out of his misery.
(Jeremy is behind Elena and heard Damon's last conversation)
Jeremy: No way in hell.
Damon: Oh, come on. It's what he would want. It's a mercy killing.
Jeremy: You are out of your mind.
(Jeremy goes away, feeling very upset - Elena goes after her brother and they're both outside the party room)
Elena: Jer, stop.
Jeremy: This is Alaric we're talking about. You know, he looked out for us, and we need to do the same for him.
Elena: No one's gonna hurt him.
(Jeremy tries to go away)
Elena: Hey. Hey. Look at me. I promise.
(Elena looks behind her)
Esther: If you wish to help your friend Alaric, I suggest you come with me.
Elena: Jeremy, go inside and get Stefan and Damon now.
Esther: I mean you no harm, but willingly or not, you will come.