Cmiiw
His ex husband bought/took him in from that brothel, and after he died Yuta took over the leadership position (?). The son in law treated Yuta like a toy bc he is technically his father's prostitute,, and bc he was supposed to take over his father's place as leader, if Yuta never joined the family.
Yuta have 2 goals. To bring the entire Kujo family down,, and to die whilst placing the guilt on Seunghyun. He's getting revenge for how the Kujo has trapped and tortured him,, and also to Seunghyun for abandoning him.

I don't understand the plot like why he go with that son in law, what's his goal, what's his past with ex husband, none of that ever showed.