Mingshu knew that Noble Lady Wei would definitely consider her proposal; after all, she had dealt with the other party for quite some time. While she couldn't say she knew her like the back of her hand, she did have a general understanding of her character.
Noble Lady Wei was not someone who valued righteousness, but rather, she was motivated purely by self-interest. To escape Consort Shu's harassment, it was only a matter of time before she would give up Zhong Changzai.
Zhong Changzai wanted to use someone else to do her dirty work, but how could she know that the knife wouldn't turn around and wound her own hand?
However, Mingshu certainly didn't believe that this would completely expose Zhong Changzai's missteps; since she dared to use Noble Lady Wei, she must have left herself a way out. Presumably, even if she was betrayed by the other party, she would have corresponding countermeasures.