How can one forgive someone who has wronged him in his heart, especially when he sees that this person is receiving divine punishment, and feels that the inability to forgive is not by his own will?

It would have been more fitting for you to forgive your friend and accept her apology after she came to you regretful, for it is in the nature of a believer to pardon and accept excuses. Allah Almighty says: "And let them pardon and overlook. Would you not like that Allah should forgive you?" Hearts should be purified for believing sisters, and hatred reserved for the enemies of Allah. Satan seeks to incite discord among believers. The Prophet, peace and blessings be upon him, said: "Indeed, Satan has despaired of being worshipped by the نماز-performing people in the Arabian Peninsula, but he will instigate discord among them." Not forgiving easily indicates hardness in the heart that should be softened. Whoever makes things difficult for people, Allah will make things difficult for them; recompense is of the same nature as the deed. Do you hope that Allah will overlook your faults or make things difficult for you? Strive against your soul and purify your heart. Your friend's tribulation may not be due to her fault, for tribulations have multiple causes, and there are reasons for averting tribulation and wisdom behind trials.