Are the children of a divorced sister, whose father does not provide for them, considered orphans? Is it permissible to give them Zakat or Sadaqah, knowing that their mother is a descendant of the Prophet (peace be upon him) through her mother's side, and is capable of working and providing for them?

These children are not considered orphans according to Islamic law, and their father is obligated to provide for them. If he fulfills this obligation, then it is not permissible to give them Zakat. If he fails to do so, then it is permissible.

As for their mother: if there is someone who provides for her, then it is not permissible to give her Zakat. If there isn't, then she may take from Zakat, and she is not obligated to earn a living.

The fact that they are relatives of the Prophet, peace be upon him, from their mother's side does not prevent them from receiving Zakat. The Household of the Prophet (Ahl al-Bayt) for whom Zakat is forbidden are the Banu Hashim and those who are associated with them.