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May I be wrong but I don't think that woman was Taeha's mom.
Supposedly, Taeha is the result of an affair between the CEO and a mistress, which is why he's called a bastard. It wouldn't make sense for his mother to be married to the CEO — if that were the case, then where would Taehee's mother be? Taehee is the one supposedly considered the legitimate son, and it makes sense that he acts superior.
Think of it this way: it would be strange for Taehee to behave so confidently if the woman married to the CEO were Taeha's mother.
An alternative would be: Taehee's mother died and the CEO married another woman — but even so, it’s still strange, because if that’s the case, why do they keep calling him illegitimate?