Is it permissible to test one's wife to ascertain her repentance after discovering her previous relationships, and does the Sharia interest necessitate her remaining [with him] if this recurs despite prior forgiveness?

If the wife repents and signs of her sincere repentance become apparent, then it is not permissible to spy on her or seek out her faults merely due to whispers (waswas), but rather one should have a good opinion of her.

However, if something suspicious appears from her, and the matter is not merely whispers and doubts, then it is permissible to spy on her, and to spy on those who are suspicious. If you ascertain that she has returned to forbidden relationships, then divorcing her is in the interest of Islamic welfare.

It is incumbent upon the husband to uphold his role of guardianship over his wife, to close the doors of temptation for her, to establish Allah's limits in his home, and to cooperate with his wife in obedience to Allah; for in that there is protection from the unlawful and security from temptations.