Salam Alaikum,

This question is regarding a child who is 21 years of age, and has discovered about her mother’s extra maritial affair

What should a person do when he/she finds out that his/her mother is cheating on his/her step-father and having relationships with another man outside marriage which is haraam.

After numerous tries to explain the mother, the discussion comes to an end when mother starts talking about suicide when asked to stop this, or when warned that it’ll be told to the father. After which the child is helpless.

What does islam suggest in such cases?

Really it is disturbing situation and difficult to handle when someone is not ready to understand and giving threat of suicide.
Discus the matter with your mother's family . May be they can assist you and mother will listen their word. And explain to mother that it is haram and talk about Azab and punishment and impact of her act on children and family
May Allah guide her and give her taufeeq to refrain herself from Haram