From what I remember, their mother tried to keep them as far away from his ears as possible. She left her parents' home on her own after having Taesung, I believe. And from her reactions, it was kind of clear she was repulsed by his behavior. And her conversation with the grandmother at the beginning of the season implies that they were expecting him to flip his shit when he found out.
I believe he only shows up in a flashback. Taesung's mom just adopted Haebom, and they got into a fight about her taking care of a kid that isn't her own. He essentially cuts her off, but tells her to leave Taesung behind (presumably because he wants an heir for his company).
I'm sure the grandfather not wanting Taesung and Haebom together is a combination of control/classism/traditional views (homophobia).

I don't remember every part of this one, after all it's been awhile :) , but anyway, maybe someone remembers it better then I do and can answer this... Did the grandfather ever show any signs that he didn't want them together? Did he ever say something, look a weird way, or anything at all that would make it have more since as to why he is being an old ass piece of shit old fart?