I don't think this really happened, at least, in this way...I remember that Minnie had been rather brutal in the way he talked to his son when they meet for the last time ...at the movie Nicholas and Alexandra. I think you are speaking about that movie and not about the real thing. She could have speak not so gentle words about Alix more than once, she even wrote letters treating this issue, but not in the crude way she did at "Nicholas and Alexandra".
However, I'm not able to remember that she had said nothing about Nicky's brothers. All she said is that Nicky's father would have hanged the chiefs of the riots. But nothing more. And remember: it's a MOVIE not the real history of the facts. Nobody knows for sure what mother and son talked about.
Olga Alexandrovna told later that her mother would blame Alicky for all bad things that were happening, but she spoke this way to her daughter, never to his son. And I don't know any entry of the Tsar's diary written in the terms you are referring to.
RealAnastasia.