What is the ruling on the son of the maternal uncle remaining in a house where there are women until late at night, knowing that the mother permits this, while the maternal uncle and his son prevent their daughters from mixing?

If the person who brought your mother home and sat with her in the house is her nephew (her brother's son), then he is a mahram to her, and it is permissible for him to sit with her alone. As for your sister, the son of her maternal aunt (her mother's sister's son) is not a mahram to her; he is a stranger to her. Therefore, it is not permissible for him to be in seclusion with her, even if a mere greeting or conversation for a necessary purpose is permissible. The overnight stay of the maternal aunt's son in your house is permissible, provided it does not lead to seclusion or suspicious mixing.