I don't remember well, but was hyesung's mother mentioned in the main story.?

Yes, she saw him on tv and went to their house but Hyesung didn't want to see her, only talked to her for a little bit through the door.

I think it was part of the main story towards the end. She wanted to see Hyesung but he refused to see her. I don't think she really meant it, but she blamed Hyesung (partially) for why they never reconnected during his childhood. I really dislike her for that. It makes me feel a little icky that Byul is hanging out with her and letting her know about Hyesung's life when she deeply hurt him.