What is the ruling on a veiled woman uncovering herself in front of her paternal nephew’s maternal uncle, or her maternal niece’s paternal uncle, or her maternal aunt’s paternal cousins? And is it permissible for her mother to greet them and consider them her brothers?

Your paternal uncle's brother is not a mahram to you, because the brother of your father's wife is not a mahram. Similarly, your maternal aunt's brother is not a mahram to you, because your mother's husband's brother is not a mahram. And the children of your mother's paternal uncle are not mahrams to you, nor to your mother.