It would look like the movie Carrie.
To get into the Halloween spirit, I've been watching movies that I only saw parts of growing up, although I wouldn't have noticed this aspect of the movie as a child even if I had seen the whole thing. Other movies, such as Heathers and Metropolitan, have shown the adolescent world devoid of parents to emphasize how little influence they have on their children -- it's how they interact with one another that matters most. (Parents can only affect kids indirectly through choices that affect the make-up of their kids' peer group.)
But few come to mind that show what would happen if patriarchal male authority vanished for any reason -- wiped out, collapsed under its own weight, atrophied due to apathy, or whatever. Carrie does. There are hardly any fathers or father figures: Carrie's left her and her mother for another woman, and we only see the father of the survivor / guilty conscience girl for a moment before his daughter runs off with no explanation for where she's going. He shrugs and lets her get away. The principal is impotent and has abdicated his authority role. We never get the sense that he's got his eagle eyes trained on his hell-raising charges, just waiting to crack down on them. Rather, through his flaccid body language and consistently getting Carrie's name wrong, he seems to be coasting through his final week at the office. He just doesn't give a shit anymore. The English teacher likewise is off in la-la land somewhere -- not so much a free spirit, with the connotation of rebelliousness that carries, but merely daydreaming to numb the pain.
The only character who approaches a patriarchal authority figure is the gym teacher, who is portrayed as a drill sergeant in dolphin shorts. It would be a mistake to see her as Carrie's surrogate mother -- she already has one, shown to be a common neurotic trainwreck of a middle-aged woman whose instability the father is supposed to protect his daughter from. The quasi-father figure of the cool-headed and authoritative gym teacher is the only sympathetic character in the whole movie.
And it's no wonder why -- just look what happens when there is no patriarchy to control female behavior! The phrase "Lord of the Flies" has long passed into popular usage to refer to how bestially males, particularly young males, will act in the absence of authority. But what about how girls will act? It's not as though they're sugar and spice and everything nice. They're just as vicious as males, only not in a violent way. They hardly need to be -- they'll just tease and ostracize and persecute each other until they feel like killing themselves. I don't think Mean Girls is up for the job, mostly because it's a comedy instead of something dark and serious.
So I nominate Carrie as the go-to movie reference when some clueless person starts babbling about how much better, even if not perfect, the world would be for women if there were more female-style rulers (i.e., not simply females playing male roles a la Thatcher or the gym teacher from Carrie). Neutral third-party patriarchal rule not only keeps young males from destroying each other; it keeps girls from going for each other's throats as well.