It is interesting that you both want the same thing for each other: you want to see a change in feeling towards the sister. That is something to remember when you feel that your fiancee is being unreasonably intrusive or asking too much of you.

Sisters, especially twin sisters, are often close. So when you attack the sister, or reject the sister, it feels to your fiancee that you are also attacking or rejecting part of her (your fiancee).

What would your fiancee need to see to conclude that you like her sister "enough"? In other words, how will she know when you are "there"?

With regard to your fiancee's self-esteem: in my opinion you must remember that you are her lover and not her therapist. Your job is to accept and love her as she is. Does she see a therapist? If so, that could be helpful and you can certainly encourage that. But your fiancee's relationship with her sister ultimately is up to your fiancee, not to you.

You said that your relationship with her sister is a dealbreaker for your fiancee. How much of a dealbreaker is it for you?