Korean Air whistle-blowers have also accused the Cho family of illegally bringing in luxury items from overseas, disguising them as company goods to avoid tariffs and to save transport expenses.
Korean Air is not the only airline to be pulled into the spotlight in recent times.
"As chairman of Korean Air and as the head of my family, I feel crushed by the immature behavior of my daughters".
epa06682727 Officials of the Korea Customs Service exit the residence of Cho Hyun-min, senior vice president of Korean Air, in Seoul, South Korea, 21 April 2018, after searching for evidence over allegations that Cho and her family didn't pay duties on luxury goods brought into the country through the company's flights.
He also said Korean Air will create a new vice chairman position to be filled by someone outside of the Cho family and will strengthen the board's role in company operations.
The notorious heiress was jailed but had returned to work as an executive of Korean Air's hotel affiliate in March.
The incident was dubbed "nut rage", prompting the sister's case to be described as "water rage".
In 2014 her older sister, Cho Hyun-ah, infamously kicked a cabin crew member off a plane after being served macadamia nuts in a bag rather than a bowl, resulting in the delay of the flight. She then ordered the plane - already taxiing and carrying 250 passengers - to return to the gate and had the offending flight attendants ejected, according to the Washington Post.
In the latest instalment, police said Monday they were looking into whether the sisters' mother Lee Myung-hee had herself abused employees verbally and physically.
She was sentenced to a year in prison, but later freed after an appeals court cleared her of the most of hampering an air route.
"I am deeply sorry that problems connected to my family have anxious the people and employees of Korean Air", he said.
Cho Hyun-min publicly apologised for the fracas, saying her behaviour was "foolish and reckless". She was accused of throwing water in the face of an advertising executive during a business meeting.
"I sincerely apologise for upsetting the general public and employees at Korean Air over issues related to members of my family", their father said in the statement. Cho Yang-ho is chairman of the Hanjin Group, the conglomerate that owns Korean Air.