...Yeah, I just wanted to call her Professor Peridot.
Ok, so to the moon to search for a control method, with Garnet's flaw about Gems probably being what makes her destroy the panel in this case.
Which then results in a "Diplomacy" check with Steven later, unless you decide to just skip that entirely.
My expectation for what's gonna happen: as another commenter said, the Gems will head to the moon with the intent of finding a method to control the Cluster. Then, Peridot's apparent hidden agenda of contacting Yellow Diamond to get her a ship off Earth and convince her to harvest the Earth's resources rather than destroying it is probably going to be Jake not wanting to let go of Peridot's villain persona, and Steven feeling betrayed is gonna play out as Finn being upset that a friend would play a villain without telling them. Then, Yellow Diamond being outed as not all that reasonable will be the GM(s) finding a natural way to get Peridot squarely into the 'good guy' group without it being rail-roady.
Wait whaaaaa... It seems we will have ["Some srious complications, my colleagues" in space french]