She passed away after being killed a year and a half before the events of Another Story.
She never physically appears in the game, but her sons most likely got their red hair from her. it's possible she may also has gold eyes, or the twins probably just got their gold eyes from their father.
She was a cruel, abusive, violent, spiteful woman who exhibits severe sociopathic tendencies. She suffers from severe alcohol addiction, and used an invective language with anybody she came across. She was portrayed as a selfish, foul, and scornful person who used violence whenever she didn’t get her way. Saeran described her as self-damaging, that whenever she got drunk, she’d get mad and end up blaming herself and the world. Because the twin's father was a high-profile and married politician, she used the fact that she was his mistress and that she had children by him to her advantage to blackmail and to extort money from him.
She never showed her sons any love and was extremely abusive to them. Her abuse was emotional, mental, and physical. And it consisted of calling her sons worthless monsters, beating them, tying them up, strangling them, starving them, and much more...
She was described by Saeyoung as outrageous, and half-insane. Saying that she never considered them as her children, but as tools to threaten their dad. While Saeran described her as an intemperate, malicious woman, who made his life a dark tunnel filled with misfortune.
She never let her sons go to school, or outside of the house because of the fear of losing them to their father. she constantly used their father's position to strike fear in them and told the twins that their father would send people to kidnap and kill them, and if it wasn’t for her, they would already be dead.
According to Saeran, She tried to protect them at all costs. And Whether or not she had genuinely loved her sons at some point in time or had only raised them into adolescents for blackmail material is unknown. However, she was hysterical when Saeyoung had disappeared to work for the intelligence agency. And it has been stated by Saeran in an outgoing phone call that she used to hold him tight all day long after everytime one of his Father’s men visited, And that even though they lived in extreme poverty, she made sure that her sons got something to eat at least once per day. 
Not much is known about her story or origins yet.
But 21 years before the events of the game, she was sexually involved with the current prime minister which resulted in the twins birth.
how she became the way she is, how she got herself in poverty, and how she got entangled with a high-profile politician remains unknown.
21 years before the game events, they had a sexual relationship, which resulted in the birth of their illegitimate children. Whether it was just sexual or if they were romantically involved remains unknown. However, they seem to know a lot about each other which implies that she may have been his mistress for a while.
The two seem to hold a strong hatred for one another. Mother Choi constantly insults him and implies that he “ruined her life” and “made her suffer”. And according to Saejoong, she put him through hell. Calling her a “drunkard” and a “witch”. Loathing being compared to her and saying she “disgusts him”.
Mother Choi used their former relationship and their illegitimate children to blackmail him for money to maintain her silence for 20 years.
Their relationship wasn’t explored as much as her relationship with Saeran.
However, he was abused a lot by her. She seemed to dislike him more than his brother due to his rebellious, and brave nature, threatening to throw him out first once she gets her money. And he seems to hold a lot of resentment towards her, avoiding and defying her most of the time.
She was aware that he was mentally and physically stronger than his brother, and due to her dislike of him, she would often send him to run errands such as buying medicine and water. being treated as more expandable by putting him more at risk of his father’s kidnappers. Fortunately, her disregard for him made him more independent and headstrong.
He was the one who wanted to break out of her abuse with Saeran and did everything in his power to do so. His disobedience and resistance to her later allowed him to meet Rika and V, which gave him the chance to study Computers and Code and finally escape her.
She was more attached to Saeran, making him her favorite child. Which resulted in him being kept more indoors, and that caused him to be more exposed to her violent outbursts and temperamental personality. That contributed to him being more sickly, weak, and pessimistic. 
Saeran is often disdainful towards his mother for abusing him. However, after Saeyoung left, he acquired some fondness toward her during a certain period, which was the result of the trauma of his twin brother’s absence. Because according to him, she “didn’t leave him as he did”. And after her death, he became grief-stricken and mourned her with a shattered heart.
Her abuse caused him a lot of mental and physical issues. Making him vulnerable and unshielded from the exploitation and manipulation he suffered after her death.
in Ray’s AE, his attachment towards her develops even more, trying to find the good in her and painting her as more sympathetic than she actually was, grows to miss her presence, and hopes of seeing her again after committing suicide in BSE 2. After knowing that she was killed by Rika, he was heartbroken and anguished, he claimed that his life turned into a storm after her death, and that even though she was ruthless and unkind, she still wasn’t evil enough to be murdered. He wept sorrowfully for her fate, and stated that he forgives her for everything she did to him.
- Mother Choi's death remains a progressing mystery to be solved throughout the course of Mystic Messenger.
- In Saeyoung's Route, the player and Saeyoung are told she committed suicide 2 years and 6 months before the Deep Routes.
- In Yoosung's Route, it was hinted at by Jaehee that she was actually killed. Players are led to assume it was by Saeran.
- However, in the Mint Eye Believer's package that players can purchase on the Cheritz store, Saeran's diary reveals that he had recently escaped the home before she died. Though it appears to potentially be a murder, investigators cannot find out who did it and chalk it up to a suicide. Saeran is seen mourning her death despite the abuse he endured from her.
- In the Good Ending of Ray's Route, it is revealed after the credits that Mother Choi was in-fact killed by Rika in self defense. Upon attacking Rika for taking Saeran away, thinking Rika is one of the Prime Minister's cronies, Rika defends herself and accidentally kills Mother Choi in the process.
- In Ray’s After Ending, it has been stated that her body was never found, because Rika wanted no evidence.
- Due to the same reason, she never got a proper funeral.
- Cheritz revealed during the Otakon 2018 panel that Mother Choi's alcoholism is the reason Saeyoung refuses to drink throughout the course of Mystic Messenger.
- Ray’s After Ending, 2nd Day, Outgoing phone call “I Was Thinking Of Saeyoung”.
- Seven's route, day 8 - Saeran;It must be so nice... Mom doesn't keep you locked inside... I wish mom would hate me too and let me go. Then I can be positive like you... I might even think that we can get out of here.
- Secret Story 2, episode 1 - Saeran;We are identical twins, but he was always stronger than me. Just because our mother liked to torture me more, I was always behind him.
Saeran;Still, I didn't care.
Saeran;If my other half was strong, it was the same as if I was strong.