Because the uke was adopted, he left his twin behind because he wanted to protect him. His roll in the beginning of the story is to represent the trauma they went through, being sexually assaulted as children, and Chung always living to repay and protect his twin brother, who took his place and was abused too. The heir is not necessarily from direct bloodline to my understanding, only partly, and Chung was taken to protect the other brother's identity (as Chung decided). His twin brother Hong, resented him for being abused and also for leaving him. So, Hong's roll is just to act as a way to represent Chung's trauma, constant abuse, erratic upbringing and also to shine a light on his forgiving, kind and caring nature to a fault. The problem with this story is that much of what we know of characters needs to be assumed through their interactions with others verbal and non verbal, because we don't get to be in their headspace nor they seem to reveal anything about themselves.

idek what his twin's role is, what did he contribute in the story? If the uke is in baek ro's bloodline then his twin too but why only the uke became the heir?