Praise be to Allah.
If you want to deal with him on the basis of justice, then it is permissible for you to respond in like to his unkind words, as Allaah says (interpretation of the meaning): "And if you punish (your enemy), then punish them with the like of that with which you were afflicted" [al-Nahl 16:126].
But if you bear it with patience, that will be better for you, as Allaah says at
the end of the same aayah (interpretation of the meaning): " But if you
endure patiently, verily, it is better for al-saabireen (the patient ones)."
If you want to turn enmity into love, then treat him well, if he treats you badly, as Allaah says (interpretation of the meaning): "The good deed and the evil deed cannot be equal. Repel (the evil) with one which is better, then verily! He between whom and you there was enmity, (will become) as though he was a close friend." [Fussilat 41:34]
The words, "The good deed and the evil deed cannot be equal" mean that there is a huge difference between the two. "Repel (the evil) with one which is better," means that when someone treats you badly, answer back with something better, as 'Umar (may Allaah be pleased with him) said: "There is no better punishment for the person who sinned by being bad to you, than your obeying Allaah by being good to him in return." (Tafseer Ibn Katheer).
A man came to the Prophet (peace and blessings of Allaah be upon him) and said: "O Messenger of Allaah, I have relatives with whom I try to keep in touch, but they cut me off; I treat them well, but they treat me badly; I try to be kind to them, but they are cruel to me." He said: "If you are as you say, it is as if you are putting hot ashes in their mouths. You will continue to have support from Allaah against them so long as you continue doing that." (Reported by Muslim, no. 2558)
Our advice to you, our sister, is to be tolerant and forgiving. Follow your mother's advice. It is clear from your question that this man has room to regret and retract his bad actions. Allaah tells us (interpetation of the meaning): " whoever forgives and makes reconciliation, his reward is due from Allaah" [al-Shoora 42:40]
However, all of this does not prevent us from protecting ourselves from the evil and harm that such relatives may cause. If going to their houses, for example, will cause some kind of offence or harm, then the relationship can be limited to telephone calls, kind words, the occasional gift and so on. The relationship can be maintained at a distance, if being too close will cause problems.
We ask Allaah to guide us all, to help us not to bear any grudges towards
anyone, and to treat one another properly. May Allaah bless our Prophet