Forgiveness doesn’t mean the crime didn’t happen, and it doesn’t mean the person shouldn’t go to prison. It means you are handing the “right to revenge” over to God so that bitterness doesn’t destroy you.
The sinner must acknowledge/confess their sin, then
The sinner must ask for forgiveness from the one they wronged for what the sinner did to them, then
The sinner must atone -- including face the conseqences -- for their sin.
It is important to consider that the one who is asked for their forgiveness can only forgive the sinner for what the sinner did to them; not for what the sinner did to anyone else. For example, in the case of a murder the victim's mother can offer forgiveness for the pain and suffering and loss the murderer caused to her; she cannot, however, the murderer for the murder itself. Only the murdered victim -- or God, of course -- can do that, on the basic principle that you cannot forgive someone for what they did to someone else.
You are right. I like the way you put it about revenge and bitterness. Let God handle it.