I feel bad for the FL. But her brother and his mother did nothing wrong.
Jimin is Joon's half-brother. His mother is not her mother. It is impossible to get custody of ex-husband's kid. It is also unfair to ask Jimin and his mother continue living with abusive father/husband just for Joon's sake.
Jimin is Joon's half-brother. His mother is not her mother.