What is the ruling on keeping one's wife or divorcing her after she confesses to adultery and repents, and what is the ruling on child custody in the event of divorce?

You must protect your family from the causes of corruption, and their falling into it was due to negligence in oversight. You must remind your wife of Allah and that adultery is one of the gravest sins, and cleanse your home of anything that leads to corruption. If your wife repents, then keep her; otherwise, divorce her, and she will not have custody of the children if she does not repent.