Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
If you want to deal with your maternal uncle on the basis of justice, then it is permissible for you to respond in like to his unkind words, as Allah says (interpretation of the meaning): "And if you punish (your enemy), then punish them with the like of that with which you were afflicted." [An-Nahl 16:126]
But if you bear it with patience, that will be better for you, as Allah says at the end of the same verse (interpretation of the meaning): "But if you endure patiently, verily, it is better for the patient ones." [An-Nahl 16:126]
If you want to turn enmity into love, then treat him well, if he treats you badly, as Allah 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 Allah be pleased with him) said: "There is no better punishment for the person who sinned by being bad to you, than your obeying Allah by being good to him in return." (Tafsir Ibn Kathir)
A man came to the Prophet (peace and blessings of Allah be upon him) and said: "O Messenger of Allah, 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 Allah against them so long as you continue doing that." (Narrated 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. Allah tells us (interpretation of the meaning): "whoever forgives and makes reconciliation, his reward is due from Allah" [Ash-Shura 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 Allah to guide us all, to help us not to bear any grudges towards anyone, and to treat one another properly. May Allah bless our Prophet Muhammad.
For more details, please see the following answers: 143596 , 324944 , 22706 , 85317 , 129319 , and 2621 .