Of course she can't say "don't go". She has to play the part of the adult.
Yeah, kinda what I was thinking. This is exactly the sort of thing where an adult can't say that, even if they think it. This is one of the places where Haru's age is a big factor. She doesn't realize quite that before everything else, Midori really can't tell Haru she wants her to stay. The circumstances - not just not being a relative, but also not wanting to use your power as an adult to influence a minor - just in every way, Midori doesn't really have anything she can do.
That is really frustrating for a kid, I think, I can see why Haru is not satisfied. She's just gonna have to read between the lines, cause Midori will indeed play by the rules here.