We're talking about killing a man just in consideration of the very small possibility he manages to escape and kill another innocent. The good doesn't seem to outweigh the bad by killing him, even if I were to allow some leeway and put less value on the murderer's life.
Yeah, cause no one ever kills in prison.

And I'm not weighing good against bad. You said "it's not going to solve anything", and I simply refuted that by saying it does permanently solve the threat that person poses to others.
Blood-thirsty, perhaps? Not inherently wrong by itself, but not an ideal mode of character to possess.
If we are talking about their
character (your words) and not simply the emotions and thoughts they are having regarding a given situation, then your assessment of their character, lacking any further information about the person, is unfounded. Just because someone thirsts for the blood of a man who raped and murdered their mother, doesn't mean they are a generally bloodthirsty person.
Well if the vigilantes have killed the murderers before they have even gone to trial then that is even worse. We certainly can't accept a general principle like "If some member of society decides a person is guilty of murder then they are allowed to kill that person". Society would turn upside down.
Correct, but, still, if I were sufficiently convinced the father and grandfather were guilty of the crime they were killed over, and I was on the killer's jury, I let them walk. The social consequences of having everyone adopt that as a general principle would not be of any concern to me in that moment-- my only concern would be that I could not morally condemn the killer for that individual act.
Clearly your view of "rights" is similar to (what I assume is) your view of good and bad actions. Rights are supposed to be absolute, regardless of the situation. Good and bad actions in general are situation dependent. If you believe that there are certain circumstances where somebody's rights can be forfeited, then it seems you never thought they had that right in the first place. That is why the concept of a person's right to life is so attractive. So you must only attach relative value to life.
Clearly my ass. An individual's rights are absolute and inviolable
until and only until that individual violates the rights of another, and which rights they lose and which they retain roughly correspond to the rights of others they have violated. Otherwise a murderer could not even be imprisoned against their will.
That isn't inherently wrong but I think that if we were to (echoing Kant) universalize this principle, so that the principle that life is only relative would be integrated into society, then in my opinion we end up with a rather unattractive kind of society...
I like Kant, but I don't buy the categorical imperative. Kant thought that lying was always wrong, for example, and that's bullshit.