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.
A person must obey his parents as much as he can and should try to combine between the obedience of both of them if they are in disagreement. If this becomes impossible, then obeying the mother is given priority to obeying the father for the Hadeeth where the Prophet said emphasizing the parents obedience when a man asked him: “Who deserves my good company more?”, and he [the Prophet] replied: “Your mother.” The man asked: “Then who?” The Prophet said: “Your mother.” The man asked again: “Then who?” The Prophet again replied: “Your mother.” The man asked again: “Then who?” Thereupon, the Prophet said: “Then your father.” [Al-Bukhari and Muslim]
But if any of the parents orders one of his children to commit a sin, then he should not obey him/her as no obedience is due for anyone who orders to commit a sin. So, if the mother orders her child to cut relations with his uncle, she is ordering him to commit a sin; severing kinship relation. In fact, Allah orders His slaves to establish the kinship relation. So, it is unlawful to obey one's mother in this matter. But one should apologize to her in a kind and soft way and if one can do this without her knowledge that would be better. Also, since the questioner knows of the difficulties between the various family members, he is advised to keep some matters to himself.
For more benefit on the limits of obedience to parents, please refer to Fataawa 271255, 131695 and 123554.
Allah knows best.