Although it was Fredo who was caught betraying his brother, it was Connie who clearly really hated Michael (although whether she was really justified in this is another question).
Two major reasons are firstly the execution of her husband and much later, indeed the killing of their sibling whom Connie clearly loved.
Despite the foregoing, she continued to have contact with Michael (who well knew why -- she needed his money and I guess he provided it out of, probably, a sense that his father would have done so and also, their mother was still alive -- but he continued to have contact with her even after their mother's death).
Was there an indication that Connie at least contemplated cutting off contact with Michael or even something more active, like revenge? And did Michael consider the possibility that she might attempt some sort of revenge for her husband or was he so sure of her dependence on him in addition to the fact that she wielded no power of her own that he discounted this possibility?