All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, try to reconcile between your mother and her brother as soon as possible. You will get great reward for that if your aim is to please Allah by such an act. Allah Says (what means): {No good is there in much of their private conversation, except for those who enjoin charity or that which is right or conciliation between people. And whoever does that seeking means to the approval of Allah - then We are going to give him a great reward.} [Quran 4: 114]
You should be wise and use the appropriate means for this reconciliation. Remind them of Allah and tell them that whoever keeps good ties with his kinship (visiting them and doing good to them) Allah will bestow blessings upon him, and whoever severs his ties with his kinship Allah will cut off ties with him; no doubt this will result in his destruction.
Allah Says (what means): {So would you perhaps, if you turned away, cause corruption on earth and sever your [ties of] relationship? Those [who do so] are the ones that Allah has cursed, so He deafened them and blinded their vision.} [Quran 47: 22-23]
Abu Hurayrah narrated that the Prophet said: "The gates of Paradise are opened on Mondays and Thursdays, and then every slave (of Allah) is granted forgiveness if he does not associate anything with Allah in worship. But the person in whose heart there is rancor against his (Muslim) brother, they will not be pardoned and with regard to them it will be said twice: 'Hold both of them until they are reconciled with each other."' [Muslim]
This is about Muslims in general. The rule will have greater impact if this is between very close relatives who are linked by very close family ties like a brother and a sister.
On the other hand, if your uncle's daughter is pious and good, do not hesitate to ask her for marriage. But this should be in an appropriate way so that your uncle who is the Wali (guardian) of the girl accepts your offer. If he accepts, that is what you desire. If he refuses because of the pressure from his wife, then try to get somebody who has an influence on them to mediate.
This might have the results you want.
Anyway, know that nothing will happen except that which Allah has predestined.
We ask Allah to guide you and us to do what pleases Him.
Allah knows best.