Of course, their mother never should have pitted one daughter against the other. That's one of the worst things a parent can do because it scars children for a lifetime.
Both actresses were great performers--on screen, of course--and Joan didn't just play mousy, vulnerable characters, either.
This article sheds a whole lot of light on the sisters' relationship. From what I can gather, there wasn't any "feud," at least not for many years and that they were both on good terms:
Sitting just a few feet away from Olivia, who was so gracious to me, and knowing how other nosy interviewers had been received, I could not muster the courage to ask her more about her relationship with Joan. But, at the end of my earlier phone conversation with Joan, who had already made several references to Olivia over the course of a perfectly coherent and interesting conversation, I felt that I had to at least try -- and I was shocked by what I was told: "This 'Olivia feud' has always irritated me because it has no basis. To this day it has no basis!"
So, I asked Joan, are the two of you friends? "Of course!" Wow -- well, I'm glad to know that, I responded. I guess some people like to sensationalize things. "Oh, right -- they have to. Two nice girls liking each other isn't copy." So today you and Olivia are in communication? You talk to each other? "Absolutely." Wow. Well, that's amazing. I'm so happy to hear that. "Oh, sure." Later in the conversation, I felt that I had to clarify what I had heard earlier. Was there ever a time when you two did not get along to the point where you wouldn't speak with one another? "Never. Never. There is not a word of truth about that." Why do you think people believe that? "Oh, I have no idea. It's just something to say." Well, that's not fair to you. "Oh, it's terrible." And have you seen Olivia over the years? "I've seen her in Paris. And she came to my apartment in New York often." I have to say that this is such a nice thing to hear because I was sad to think that you two were on poor terms. "Let me just say, Olivia and I have never had a quarrel. We have never had any dissatisfaction. We have never had hard words. And all this is press."
I would like to believe that Joan's account, rather than the decades of media reports to the contrary, represented the truth about the nature of the sisters' relationship. But unless Olivia, Deborah or Joan's assistant during her later years, Susan Pfeiffer, wish to share their own perspectives, I suppose we'll never know for sure.
I believe it was most likely the two were on friendly terms; after all, Joan's autobiography, written when she felt hurt over her mother's death, was written some 35 years ago. A lot can change over that time.