Will God punish me or will I be considered excused if I abandon my relatives because of their injustice and slander, knowing that deeds are presented to God on Mondays and Thursdays, but are postponed for those who are quarreling?

The hadith referred to concerns a Muslim's boycott of another Muslim in general, and is not specific to boycotting a relative. If the boycott is between relatives, the matter is more severe, because Islamic law commands maintaining ties of kinship even if they have wronged you. If no harm results from maintaining ties with these relatives, then it is obligatory to maintain ties with them, even if only by greeting them, and boycotting them incurs a warning [of punishment]. However, if harm results from maintaining ties with them, then it is permissible to abandon them for a legitimate শরعي benefit. Forgiveness is better and increases a Muslim in honor, and it is a means of attaining Allah's forgiveness and pardon, just as maintaining ties of kinship increases sustenance and life.