Assalamo Alaykum!
May Allah bless you for spreading awareness of our religion and answering our troubling queries!
1)- A person wronged someone by calling him bad names and then he wanted to repent sincerely for his sin. So, he went to the one whom he had wronged and asked for forgiveness but the wronged one refused to forgive him. In this case, how true repentance can be achieved please guide!!
2)- In the past, a husband treated his 2nd wife very badly by beating her and torturing her emotionally; the wife reacted to this oppression only by cursing and calling him bad names on his face directly. The husband lives with his 1st wife and he comes to the house of 2nd wife only to see his children. Now the 2nd wife, despite that she was wronged in the past by the husband, she wants to repent because she cursed her husband and called him names. Should she ask her husband to forgive her (because she is afraid of anger of Allah). Note that the husband doesn't speak to her much and he never has asked her to forgive him.
Please answer my these question because it is very sensitive matter for the person concerned and it is keeping that person awake all night because of fear of Allah!!
May Allah bless you for your noble work!!!

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

There is no doubt that a sincere and complete repentance if one wronged a human being in regard to his/her material or moral rights, requires that the transgressor should seek forgiveness from those whom he wronged as we clarified in Fataawa 87903 and 86527.

The transgressor did well by seeking the forgiveness of the man whom he wronged, and that man should accept his apology. Therefore, we advise him to continue in trying to convince the wronged person to forgive the person who wronged him even by seeking the help of someone whom he thinks may influence him, so that he would remind him about the excellence of forgiving others, like by reminding him with the Saying of Allaah (which means): {And whoever pardons and makes reconciliation his reward is [due] from Allaah}[Quran 42:40]; and the saying of the Prophet : "And Allaah does not increase the one who pardons except by more honor." [Muslim] If he forgives him; then this is what is required, otherwise, he should supplicate for him and seek Allaah’s forgiveness for him hoping that Allaah would make him pleased with him. This is in regard to the first question.

As regards the second question, then each spouse should have good marital relationship with the other and they should not mistreat each other; Allaah Says (what means): {And due to the wives is similar to what is expected of them, according to what is reasonable.}[Quran 2:228]

Therefore, if this man mistreated and beat  his wife, and he harmed her psychologically without right, then she has the right to treat him likewise in order to avenge him; Allaah Says (what means): {Allaah does not like that the evil should be uttered in public except by him who has been wronged.}[Quran 4:148]

When Shaykh Ibn ‘Uthaymeen commented on the Hadeeth in which the Prophet said: “When a wife spends the night while refusing to have sexual intercourse with her husband, the angels would curse her till the morning." [Al-Bukhari and Muslim], saying: “The wordings that are mentioned in this Hadeeth are general, but they are restricted by him fulfilling her rights, but if he does not fulfill her rights, then she can avenge him and she may refuse to fulfill his right in the same manner that he refused to fulfill her right, as Allaah Says (what means): {So whoever has assaulted you, then assault him in the same way that he has assaulted you.}[Quran 2:194]” However, if she exceeds the limits and she curses him for instance, while he did not curse her, then she is obliged to seek his forgiveness for this.” [End of quote]

It should be noted that if that woman is still in marital bond with her husband, then he is obligated to be just between her and his first wife. If he had wronged her or harmed her without right, he is also obligated to seek her forgiveness.

Allaah Knows best.