She was first mentioned in a call, which interrupted Yui as she attempted to confess her feelings to Hachiman and Yui hurried home after her mother did something. She was formally introduced in Episode 13 of season 2 where she brings tea for both Hachiman and Yukino who came to their house with Yui.
Mrs. Yuighama seems to be lenient, kind, friendly person being mostly like Yui herself. She already knew Hachiman by his nickname "Hikki", mentioning how Yui is always talking about him causing Yui to become highly embarrassed and push her out of the room.
She also recognized Yukino as "Yukinon" and asked Yui if she is required to prepare the futon for Yukino for the night stay, indicating that Yui freely talks to her mother about her daily basis. Yukino is openly envious of Yui's free relation with her mother.