How unfortunate for everyone. Both women are making a big mistake. It’s never wise to ask someone to choose between people he loves. It’s not necessary. You can love your sister. You can love your wife. Even if they don’t love each other.
You are not “taking sides” by staying connected to them both. Even the language of “sides” implies that there are irreconcilable differences. There are not. They both love you. You love them both. It is not “taking sides” for you to marry the woman you want to marry. It is not “taking sides” to want to stay connected to your sister.
It’s sad that your sister can’t be happy that you have found love. It’s also sad that these two women can’t just be polite with each other for a few hours now and then just because they love you. They don’t need to be best friends or even casual friends to do that. Sometimes the way to show love to someone we love is to accept the people in his life even if it is uncomfortable.
Get out of the middle. Tell them both as gently and respectfully as you can that you won’t choose between them because they are both “family” for you. Add that you hope with all your heart that they will just tolerate each other now and then for your sake. Tell them that you will no longer talk about their difficulty with each other. They need to work it out. Never ever say anything bad about either one to the other. That will only get you back in the middle.
Continue to see your sister. Follow your own heart and mind in deciding who to marry.
I wish you well.