I think you got it wrong. The teenage girl that thinks she's being sold off to the Beom family is actually a flashback memory of the mother when she was young. Her family was trying to marry her off to Teaha's father!
As for Hae-soo, the older brother (Taehee) is actually trying to lure her into his grasp by sending one of his men to the hotel job she works, and propositioning her boss for any extra employees she may have available to work this "emergency position" they need filled. Taehee is going to have her work at that lounge he routinely frequents for drinks and prostitutes!
Keep in mind, during all of this, Hae-soo has never told Taeha that she was looking for extra work to gain more income to get a new apartment. He has no idea what is about to happen to her if she takes this fake "new job". This is a perfect underhanded plan for taehee to subtly snatch Taeha's woman from him.
I'm not going to lie, I got confused at first with that teenage girl, but I saw that she had a striking resemblance to the boys' mother. That's when I realized the author started telling her side of the story and how she got involved with the Beom family. The author is weaving her juvenile backstory into the current storyline every now and then, however, they're not doing it in a way that readers can pick up on easily. I still have to reread certain sections of each chapter where it's done two or three times to catch the transition.

I AM SO LOST