Does the maternal uncle have the right to intervene in family affairs, and is it permissible for the mother to grant him authority for advice and guidance?

If the uncle's intervention is in the form of advice, guidance, and teaching, then there is no harm in it, and he will be rewarded for it. The mother's permission for him to give advice is not a condition, because he is divinely authorized to do so. However, if his intervention involves coercion and threats, then the uncle has no guardianship over his sister's minor children, whether male or female, unless he has been appointed as their guardian. He has no guardianship whatsoever over those who are adults. There is no harm for the mother of the children to seek her brother's help in fulfilling the family's needs.