She's playing some 4D chess here. There are several conclusions that come to mind, but this is what I believe to be the most possible.
A) She believes that Chiyo is a threat as a potential rival and she wants to get rid of her without doing anything drastic. One possibility is that because both parties has fallen in love with Rokudou, Chiyo will most likely prioritize Rokudou over her mother.
B) She knows something about the eyes that he doesn't. She knows so much in so little time and it is too similar to her daughter.