When Hiro was born, she didn't reject him nor became over-protective of him, instead simply saying that she loves the sheep. She broke the barriers of all Sohma mothers having possessed children.
According to Hiro, his mother is a klutz, always not watching her steps and falling down. She's also extremely cheerful and very kind-hearted, especially towards her children.
Fruits Basket (Manga)
Hiro got a call from his mother that she was pregnant. Shigure made a pervy quote: "Ahh, Satsuki san, so young...". This comment made Hiro very angry.
It is said that she gave life to Hinata, Hiro's sister, sometime after the Sohmas had their summer vacation.
When Hiro's curse broke, he was in the same room as Hinata, playing with her. Hiro immediately hugged her and indeed, he did not transform, meaning his curse did break. His mother comes in and gets moved. Then hugs Hiro and Hinata together.
She gets along with her son very well. Her son worry's about her clumsyness overall.
She gets along with her daughter very well.
- She doesn't appear in the anime.
all information on Sohma Satsuki came from http://fruitsbasket.wikia.com/wiki/Satsuki_Sohma