Sabrina's mother never received a proper name in the series, though she's a memorable one-off character from the episode "Haunter versus Kadabra." She's best known as the mother of Sabrina, Saffron City's Gym Leader—and as someone who learned the hard way just how powerful her daughter's psychic abilities really were.
Years ago, when Sabrina was just a kid, both her parents tried to stop her from messing around with some golf clubs. But Sabrina's psychic powers were already too much to handle. Rather than listen, she turned her mother into a doll and stuck her in a dollhouse. Her father managed to escape, though.
By the time the main episode rolls around, Misty and Brock have also been turned into dolls and trapped in the same dollhouse. Despite being miniaturized, the three of them could still talk to each other. Notably, Sabrina's mother held no grudge—she genuinely believed her daughter would snap out of it and turn them all back to normal eventually.
Things changed when Ash showed up and challenged Sabrina to a Gym battle. Ash won, and with Sabrina finally defeated, she restored everyone to their normal size and form. The episode ends with Sabrina's mother waving goodbye as Ash and his friends head out of town, restored and ready to move on.
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