Misato's approach to getting Shinji out of his shell is to badger him relentlessly until he finally cracks. He proceeds to vent that he hates being a pilot, is worried how the other kids at school will treat him, resents his father's manipulation of him, and complains that Misato's apartment is really messy.
The players immediately put Shinji into therapy, as his most memorable moments have been him losing his mind, being tormented with questions of existential guilt or masturbating to a comatose girl. Misato's monologue says it all:
"You don't really know this kid all that well yet. Normally you'd start the first day with some light teasing, maybe a game of beer cap checkers to lighten the mood. But one look at him and something deep in your soul told you he needs all the therapy."
Friends and Figurines Arc
Misato's terrible sense of direction rears its head when she takes Shinji and Rei on a hiking trip. Within half an hour, the children are exhausted and thirsty. After several hours of wandering fruitlessly, Section Two arrives to airlift them out and they all spend the next day resting.
The Red Demon Arc
Misato learns of Rei's lack of interest in womanly beauty products and luxuries and tries to drag her into a beauty parlor. Rei gives her such a disdainful Kubrick Stare that the older woman immediately decides it isn't worth it.
"You scrap the idea before you take anymore SAN damage."
Misato leaves Asuka, Shinji, and Rei to get acquainted for a few minutes while she deals with an obstructive military commander, reasoning that they'd probably be fine for that period. She returns to find Asuka and Rei trying to beat each other into submission while Shinji watches from the side.
Moving Pains Arc
Upon moving into the inn, the group is faced with the realization that Rei has no concept of modesty or sexual taboos and often walks around nude or in her underwear. Misato's efforts to educate Rei on social norms are stymied by the girl's complete lack of instinct for this sort of thing, to the point that she has to take a trip to the library to get educational books on the subject.
Misato becomes irritated when some papers she files are rejected because she forgot to mention that she is single and guardian of several children. Their response is prompt:
"They subvert the NERV supply chain and sneak in the purchase of the world's tiniest violin, which is subsequently delivered to your house. Rei thinks it's interesting."
In an otherwise tension-filled scene, Misato brings Kaji, Rei, and Kaworu together to confront the latter on his nature as the soul of Adam. Despite Misato's preexisting bias against Angels, she deals with it with some darkly comedic logic.
"Adam. The being that killed half the world, starting with your father. A titan made of white light with wings that burn out the sky. You're pretty sure Kaworu isn't Him. In the time he's been staying with you, he's destroyed very few continents."
During the otherwise deadly serious battle with Kushiel, the Angel's Mind Rape effects on Ritsuko result in this little gem:
"Ritsuko tells you that the MAGI calculate a 100% probability that she's a dirty little harlot."
The Future Soon Arc
Kaworu interrupts Mari's counter-lecture against Asuka's thermal expansion joke by using his powers to effectively dunk her with a wave of water. Mari retaliates by tackling him for a play-fight, and Rei casually brings up a hand to cover Shinji's eyes.