How do you handle a rude friend of a close friend, without damaging relationships?

One of my closest friends (Jane) has another friend who’s been in her life for some time. There are occasions when it’s necessary to include her in plans, like birthdays, etc.

The problem is that this other friend is extremely rude to me, without reason. I’ve always been kind to her, in spite of her behavior. I continually have reached out to her, joke around with her and have always tried to be inclusive in case she’s feeling jealous or possessive. I’ve continued to take the high ground despite the fact that she’s blatantly bitchy to me, cuts me off when I’m speaking, ignores me, talks over me and goes out of her way to be as nasty as possible. In some cases she’s been so nasty, it makes things awkward for everyone else. Quite frankly, I don’t want to deal with this anymore, but I don’t want to stop spending time with one of my dearest friends.

I’ve talked to Jane about this twice and she’s apologized at length. She sees and recognizes this behavior, validates that her friend is being inappropriate, but has a highly avoidant personality and doesn’t want to deal with it. As a result, she just tries to separate activities because we don’t get a long.

My point is that it’s not that we don’t get along because of something I’ve done. Her friend is out of line. She knows clear well that her friend is going out of her way to treat me badly, and she should tell her it’s not okay. She won’t do this because she doesn’t want to deal with the confrontation, and instead, complicated plans are constructed so that we don’t spend time together. This pops up and causes drama at multiple times throughout the year. I just don’t want to deal with it anymore.

What’s the most appropriate way to handle this? It really needs to stop, but I don’t want to stand up for myself only to not have our mutual friend back me up. Plus, this is her friend and I really think she needs to pull her aside.

I’m really sorry this is soooooo long, but hopefully it makes sense