What is the ruling on concealing a wife's adultery after she has repented and abandoned the sin? Is what happened considered a trial for the husband? How can the husband live with this situation? And what is the divine wisdom behind this happening despite the husband's prayers for the protection of his family?

If your wife's repentance from the indecency she committed appears to be sincere, then cover her fault and keep her. Covering the fault of a repenting Muslim is legally required, and repentance erases what came before it. Patience and turning away from dwelling on the past are aided by the certainty that Allah has wisdom in His decrees. The fulfillment of supplication is not limited to achieving what is requested; evil may be averted, or it may be stored for the Hereafter. Supplication is a means, but it does not dispense with taking other measures such as guardianship and shielding one's family from causes of corruption.