The OP is raising two, very different questions.
1) Do you support civilians meting out justice
2) Do you think the point of jail should be rehabilitation, prevention (scaring people away from committing crimes) or revenge/justice depending on your perspective.
1) In cases that are not really serious enough to warrant police consideration, it can be a good idea. A shop owner may get better results talking to a young thief's parents rather than calling the police. But for serious cases of violence? The sorts of people who are liking to do what you are suggesting will be looking for revenge.
2) Rehabilitation, every time. Prevention is stupid - the majority of crimes are committed because the person either needs money to support themselves and their family, or because they do not think about the consequences of their actions. Rehab is obviously the best because it reduces the amount of crime in the long term. What you describe as justice, shows that your morality is so radically different to mine that I doubt we'll be able to have any meaningful conversation, in all likelihood. Murder is not a suitable response to murder. If the government makes the claim that Person A murdering person b is fine because person b murdered person c, you have a preposterous legal system that cannot rationally be defended
