Based on the fact that death is both the cause and consequence of revenge, how does this apply to Hamlet and Laertes' quests for vengeance? Are they justified in their attempts to redeem their family, or are they blinded by their need for revenge?

Both Hamlet and Laertes are indeed powerfully driven by thoughts of revenge against the killers of their fathers. The death of their respective fathers would undeniably cause the two young men to experience emotional upheavals, especially since there seemed to be a good and respectful relationship between father and son in both cases. Moreover, the knowledge that the deaths of their fathers were unnatural and, in their eyes, unjustified would have created a sense of wrong done to them personally, a wrong that needed to be set right.
This is a basic human feeling, which underlies the principle of “an eye for an eye”, recorded as early as during the ancient Mesopotamian kingdom, in the form of the Code of Hammurabi. The death of a loved and respected significant someone is painful, at the least, but can be devastating. However, although Hamlet and Laertes share the same yearning for revenge, they have different perspectives and approaches.
Hamlet has a strong sense of conscience. He searches relentlessly for clear evidence of the murderer’s identity, even though his father’s ghost was the one who revealed it was his uncle, the incumbent king, who perpetrated the ghastly deed. This makes Hamlet procrastinate and put off his plans of revenge. Death is a grave matter, and to Hamlet, he has to be careful that he is doing the right thing.
In addition, the prince of Denmark has fine sensibilities, no doubt inculcated as part of his refined royal upbringing. He finds the drastic change in the state’s situation, his family circumstances and his personal life so disturbing that he contemplates, “To be or not to be…” Clearly, he is overwhelmed by depression, even paralysed to some extent.
Laertes on the other hand is absolutely vilified at the news of his father’s death, and the circumstances surrounding it, according to King Claudius’ words. He gives in too easily to his anger and becomes easy prey for Claudius to manipulate and exploit. He is too eager to embrace killing to appease his sense of loss. Hence, he naively becomes the scheming king’s instrument to get rid of this thorn that plagues Claudius' royal but corrupted throne.
To be fair, Laertes is also driven to revenge by the tragic loss of his sister, Ophelia, for whose madness and drowning he blames Hamlet. However, that is the weakness in Laertes’ case, on the question of justification. The impulsive young man is too much blinded by his fury to be willing to seek the truth. A mitigating factor is that Claudius is a very cunning and influential man, who even managed to manipulate Laertes’ father, Polonius. If the father can become Claudius’ puppet, what more the son. Nevertheless, justification for Laertes vengeful thoughts against Hamlet is much less than those of Hamlet against Claudius.
While Hamlet slew Polonius by accident, thinking it was the evil king, Claudius murdered Hamlet’s father in cold blood and with pre-meditation. The murder was motivated by greed and lust, greed for power and lust for his sister-in-law, Hamlet’s mother, Gertrude. It was a corruption that seemed to even infect the whole state of Denmark. So, in Hamlet’s case, it was not just a straightforward issue of appeasing his anger, of easing his anguish, but also saving the kingdom, and his mother.
In conclusion, while the weight of death makes Hamlet pause and contemplate, even pushing him to the bounds of uncertainty. death is readily sought by Laertes, and that drives the play to its quick and tragic ending, the consequent deaths of the innocent as well as the guilty. And while it is understandable why Laertes is so obsessed with vengeance against Hamlet, it is far less justifiable than Hamlet’s antipathy towards his uncle, the evil and corrupting usurper of his father’s throne.

It could almost always be argued that someone is blinded by revenge when they endeavor to kill someone, even under the circumstances of (arguably) just cause. In Hamlet's case, he wants to kill Claudius because his father's ghost alleges that Claudius poisoned him. Hamlet's staged play depicting these events confirms this suspicion. Now, even if it is acknowledged that Hamlet is indeed justified in his attempt at avenging his father's death, perhaps the best argument for the fact he might be blinded by revenge is when, given the opportunity, he doesn't in fact kill Claudius, for fear that he will not go to hell. Hamlet states:

Now might I do it pat, now he is praying;And now I'll do't. And so he goes to heaven;And so am I revenged. That would be scann'd:A villain kills my father; and for that,I, his sole son, do this same villain sendTo heaven. (3.3.1)

It can be said here that Hamlet is obsessed with revenge rather than justified, because he wants Claudius not only to die, but to suffer in hell (rather than heaven).
This of course leads to Hamlet's accidental murder of Polonius, which infuriates Laertes. Laertes is hell-bent on revenge, as evidenced in his following speech:

To hell, allegiance! Vows, to the blackest devil!Conscience and grace, to the profoundest pit!I dare damnation. To this point I stand,That both the worlds I give to negligence,Let come what comes, only I'll be revengedMost thoroughly for my father.(4.5.148-154)

While both are probably justified for their revenge (as losing one's parent to an untimely death is as worse a fate as one can imagine), both are obsessed with revenge in their own way. Hamlet needs Claudius' death to be perfectly times, and Laertes is himself very hot-tempered and resolves to kill Hamlet as quickly as possible.