Should I divorce my wife after she admitted to having a phone relationship and exchanging pictures with another man, or should I forgive her and overlook the matter, especially given the presence of two children and my inability to accept what happened?

If a wife betrays her husband in his absence, she has committed a grave error, and she must perform sincere repentance. If she repents and becomes righteous, then the husband should treat her well and be keen on protecting her and raising her in accordance with the religion.