Siblings do not always like each other nor get along.
I know.
I have a sibling, the eldest, that was JUST like your eldest.
When I was born, ever since I was born, she was just a monster to me. ALL our life. ALL the time. She was just, mean. To me.
Once we became adults, well one day, after my Dad died, she told me she hated me. Like I didn't know. And it was all because, she said she was jealous and that she resented me when I was born.
Oh well. Too bad. That is HER problem.
But she made it "my" problem.
Sure my parents tried ALL sorts of things to curb it or stop it. But... to a certain extent, it is and was just her personality. Not all people, are jealous or mean or treat another that way. Not everyone gets resentful etc.
You need to talk to your eldest. And get to the ROOT of the problem. Its not like you can just get rid of one child just because the eldest cannot cope. Or send her to a Therapist. Really.
And the other thing is, being the "target" of an eldest sibling like that, REALLY MAKES life MISERABLE, for that other sibling. So you ALSO have to, look OUT for, that child that is constantly being picked on and targeted. Because, this is VERY TOXIC, for that other sibling.
Me and my sibings were all raised the same. My parents never favored any kid over the other. But my eldest sibling just made life miserable for me and decided for herself, that she was going to pick on me. But it was HER... who had a personality problem.
Later in life, as an adult now... she actually went to a Therapist. And so now... it seems to help.