No, her adoptive father is not the girls dad. He was married to the mother of the girl. But divorced. And the mom found a different partner who is hyesungs best friend.
So-yi’s dad, who is Dojin’s brother, never had a child of his own. So-yi is his only child, and she is adopted.
Thanks for the explanation
Another note, the biological father of So-Yi's crush is friend of Hyesung (Byul's mom)
So-Yi has a crush on the daughter of her adoptive Father and she didn't know that, because her father doesn't have contact with his biological daughter and never talked about her.