How can the Hadiths be reconciled that speak of a believer's affairs all being good, in prosperity and adversity, and that hastening punishment in this world is good for the servant, and that punishment in this world is an expiation, with the Hadith that indicates that Allah may hasten the punishment in this world for those who commit injustice and sever kinship ties, while also reserving punishment for them in the Hereafter?

There is no contradiction between the hadiths related to the hastening of punishment in this world. The first hadith is general ("If Allah wishes good for His servant, He hastens his punishment in this world"), meaning that affliction expiates sins. However, this does not negate that some sins, such as oppression (baghi) and severing ties of kinship (qati'at al-rahim), incur both worldly and otherworldly punishments, and the former does not nullify the latter. The Prophet, peace and blessings be upon him, forbade wishing for affliction or supplicating for the hastening of punishment in this world. Rather, one should supplicate for well-being (al-afiyah) in this world and the hereafter, because the punishment of this world is unbearable, and seeking well-being is better.