From Bulbapedia, the community-driven Pokémon encyclopedia.
Rachel (Japanese: レイ Rei) is a minor recurring character in the Pokémon anime. She is Jin's wife and assists the Mossdeep Space Center as a mission control operator. Rachel is also the mother of the Mossdeep City Gym Leaders Tate and Liza.
She made her debut appearance in It's Still Rocket Roll to Me!, where she was rushing out of the Mossdeep Gym to make it to the local Space Center. The group decided to follow her there and later encounter the twin Mossdeep Gym Leaders. Meanwhile, Rachel kept watch over the impending shuttle launch as her husband prepared for his next space voyage. Team Rocket hijacked the rocket launch, though her son Tate was able to deal with the trio and land the craft safely.
During Solid as a Solrock, Rachel acted as the referee during Ash's Mossdeep Gym challenge. Team Rocket gatecrashed the battle and stole Tate and Liza's Pokémon, partially destroying the Gym in the process. Though the match resumed outside at Rachel's suggestion, which Ash won and earned himself the Mind Badge.