My solution

Option 1

If I was caroline, I would first think what Loise's problem is. It wouldn't be hard to know that Loise is jealous of me(Caroline). I would feel very terrible. I would wish loise to be  just the same as me so there wouldn't be any differences between me and her. To solve this problem, I would try to talk to Louise. But I can be sure that she wouldn't allow me talk with her. So, I would write the letter having my real thoughts and feelings to make my sister moved. If my sister seems to be impressed with my letter, I would talk to her really carefully and not hurt her feeling. And then, I'd persuade her and everything would be okay.
(Maybe not this easy..........)