Is it permissible to use jinn and some Quranic verses to reconcile a husband and restore him to his wife and home for good, and if not, are there any verses from the Quran that accomplish this?

It is not permissible to seek assistance from jinn to reform a husband or to make him love his wife again, as this is a type of magic called "atf" (enchantment or charm), and it is shirk (polytheism). Ahmad and Abu Dawud narrated from Ibn Mas'ud that the Prophet, peace and blessings be upon him, said: "Indeed, incantations, amulets, and at-Tiwalah are shirk." Ibn Mas'ud explained at-Tiwalah as something women make to endear themselves to their husbands.

Furthermore, a husband's aversion might be due to the wife's shortcomings in obeying her husband or her Lord. Both spouses must fear Allah and advise each other.

If the husband's aversion is due to magic or possession, then there is no harm in performing ruqyah shariyyah (Islamic exorcism/incantation).