Is it permissible to give Zakat al-Mal to my divorced sister to help her prepare her daughter for marriage, given that the girl's father, who helps them, is present, and knowing that I do not know if the money is for necessities or for luxuries?

Zakat is only paid to those who are deserving of it. It is not permissible to pay it while in doubt about the recipient's eligibility. If it is paid to someone who is not deserving, it is not considered sufficient, unless it later becomes clear that they were indeed a rightful recipient. Therefore, it is not permissible to pay any Zakat money for the marriage of a niece except after thorough investigation and certainty, or a strong presumption, that she does not possess what would enable her to prepare for it. In such a case, it is permissible to pay her Zakat to the extent needed for her preparation, without extravagance.