Is it permissible for a girl to appear before her brother's relatives through suckling, such as his grandfather, maternal uncle, and paternal uncle, knowing that she is his sister through suckling and he nursed from her mother, but she did not nurse from his mother?

You have no relation to your brother's lineage through rada'a (nursing), such as his father, paternal uncle, or grandfather, nor to his collateral relatives like his brother or sister. This is because the prohibition (of marriage) extends only from the nursed child to his own offspring, and does not extend to his brothers or sisters, nor to those higher in lineage like his father, mother, paternal uncles, paternal aunts, maternal uncles, or maternal aunts.