Bear in mind, too, that Molly eloped with Arthur, and appears to have done so right out of high school.
Wizards are considered of age at 17. Yes, the Weasleys were overprotective of the underage Ginny—almost ridiculously so—but if, when this story takes place, Ginny is legally an adult, I think she's unlikely to tolerate being treated like a child. She doesn't tolerate it very well when she is a child. And if she's already out of school, she's fairly likely to tell Molly to get stuffed, quite possibly in so many words.