What is the described type of killing, and what must those involved do to repent, knowing that they killed a man by stabbing him with knives and striking him with a cleaver in revenge for their father, and will their repentance and good deeds benefit them after the victim's guardians have refused reconciliation?

Killing with knives and striking the head with them is intentional murder, because it falls under the category of actions highly likely to cause death. This is what the jurists defined as intending to kill a known, inviolable human being by means that are highly likely to cause his death. The repentance of the killer does not waive the right of the victim's guardians to retribution (qisas), nor the right of the victim himself on the Day of Judgment.