What is step mother’s problem tho? What is the lore behind their relationship

Probably something as simple as her step son dominates her own sons and she can’t have that. Her whole line started with how noble her family line was and how Shin’s wasn’t so she took him in never expecting he’d basically stand above her sons.

If I may add, it also has to do with the company succession I think. Traits, I believe, is a huge factor on who the board favors. Since Shin is a dominant alpha, he surpasses even his own father, I think. Everything will be basically at Shin's hands once he graduates and starts working.