"Who knows what really went on as according to Rue they(Beat and betty) got along fine"
Well, that's not exactly accurate. Rue does describe Bea calling Betty a horrible name and being pissy about Betty, in Rue's book "My First Five Husbands". She tries to be tactful about it, but makes it clear that the animosity came from Bea's direction, not Betty's. Bea was also not always nice to Rue herself, but Rue went out of her way to tell a story where Bea showed her much kindness right after Rue lost her father. (what half-way decent person wouldn't, however)